From 1b4a1dccb7ef68212e89833e4956e8eebc3af8b9 Mon Sep 17 00:00:00 2001
From: David El Malih <david@billiv.fr>
Date: Wed, 12 Nov 2025 23:20:39 +0100
Subject: [PATCH 1/3] refactor: enhance type hints and documentation in
 EulerDiscreteScheduler

Updated type hints for function parameters and return types in the EulerDiscreteScheduler class to improve code clarity and maintainability. Enhanced docstrings for several methods to provide clearer descriptions of their functionality and expected arguments. This includes specifying Literal types for certain parameters and ensuring consistent return type annotations across the class.
---
 .../schedulers/scheduling_euler_discrete.py   | 241 ++++++++++++++----
 1 file changed, 190 insertions(+), 51 deletions(-)

diff --git a/src/diffusers/schedulers/scheduling_euler_discrete.py b/src/diffusers/schedulers/scheduling_euler_discrete.py
index f88b124f04e7..0c732e7b515e 100644
--- a/src/diffusers/schedulers/scheduling_euler_discrete.py
+++ b/src/diffusers/schedulers/scheduling_euler_discrete.py
@@ -97,7 +97,7 @@ def alpha_bar_fn(t):
 
 
 # Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
-def rescale_zero_terminal_snr(betas):
+def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:
     """
     Rescales betas to have zero terminal SNR Based on https://huggingface.co/papers/2305.08891 (Algorithm 1)
 
@@ -146,17 +146,17 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
             The starting `beta` value of inference.
         beta_end (`float`, defaults to 0.02):
             The final `beta` value.
-        beta_schedule (`str`, defaults to `"linear"`):
+        beta_schedule (`Literal["linear", "scaled_linear", "squaredcos_cap_v2"]`, defaults to `"linear"`):
             The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
-            `linear` or `scaled_linear`.
+            `"linear"`, `"scaled_linear"`, or `"squaredcos_cap_v2"`.
         trained_betas (`np.ndarray`, *optional*):
             Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
-        prediction_type (`str`, defaults to `epsilon`, *optional*):
-            Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
-            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
+        prediction_type (`Literal["epsilon", "sample", "v_prediction"]`, defaults to `"epsilon"`, *optional*):
+            Prediction type of the scheduler function; can be `"epsilon"` (predicts the noise of the diffusion process),
+            `"sample"` (directly predicts the noisy sample`) or `"v_prediction"` (see section 2.4 of [Imagen
             Video](https://imagen.research.google/video/paper.pdf) paper).
-        interpolation_type(`str`, defaults to `"linear"`, *optional*):
-            The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be on of
+        interpolation_type (`Literal["linear", "log_linear"]`, defaults to `"linear"`, *optional*):
+            The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be one of
             `"linear"` or `"log_linear"`.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
             Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`,
@@ -166,18 +166,24 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
         use_beta_sigmas (`bool`, *optional*, defaults to `False`):
             Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
             Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
-        timestep_spacing (`str`, defaults to `"linspace"`):
+        sigma_min (`float`, *optional*):
+            The minimum sigma value for the noise schedule. If not provided, defaults to the last sigma in the schedule.
+        sigma_max (`float`, *optional*):
+            The maximum sigma value for the noise schedule. If not provided, defaults to the first sigma in the schedule.
+        timestep_spacing (`Literal["linspace", "leading", "trailing"]`, defaults to `"linspace"`):
             The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
             Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
+        timestep_type (`Literal["discrete", "continuous"]`, defaults to `"discrete"`):
+            The type of timesteps to use. Can be `"discrete"` or `"continuous"`.
         steps_offset (`int`, defaults to 0):
             An offset added to the inference steps, as required by some model families.
         rescale_betas_zero_snr (`bool`, defaults to `False`):
             Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and
             dark samples instead of limiting it to samples with medium brightness. Loosely related to
             [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
-        final_sigmas_type (`str`, defaults to `"zero"`):
+        final_sigmas_type (`Literal["zero", "sigma_min"]`, defaults to `"zero"`):
             The final `sigma` value for the noise schedule during the sampling process. If `"sigma_min"`, the final
-            sigma is the same as the last sigma in the training schedule. If `zero`, the final sigma is set to 0.
+            sigma is the same as the last sigma in the training schedule. If `"zero"`, the final sigma is set to 0.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -189,20 +195,20 @@ def __init__(
         num_train_timesteps: int = 1000,
         beta_start: float = 0.0001,
         beta_end: float = 0.02,
-        beta_schedule: str = "linear",
+        beta_schedule: Literal["linear", "scaled_linear", "squaredcos_cap_v2"] = "linear",
         trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
-        prediction_type: str = "epsilon",
-        interpolation_type: str = "linear",
+        prediction_type: Literal["epsilon", "sample", "v_prediction"] = "epsilon",
+        interpolation_type: Literal["linear", "log_linear"] = "linear",
         use_karras_sigmas: Optional[bool] = False,
         use_exponential_sigmas: Optional[bool] = False,
         use_beta_sigmas: Optional[bool] = False,
         sigma_min: Optional[float] = None,
         sigma_max: Optional[float] = None,
-        timestep_spacing: str = "linspace",
-        timestep_type: str = "discrete",  # can be "discrete" or "continuous"
+        timestep_spacing: Literal["linspace", "leading", "trailing"] = "linspace",
+        timestep_type: Literal["discrete", "continuous"] = "discrete",
         steps_offset: int = 0,
         rescale_betas_zero_snr: bool = False,
-        final_sigmas_type: str = "zero",  # can be "zero" or "sigma_min"
+        final_sigmas_type: Literal["zero", "sigma_min"] = "zero",
     ):
         if self.config.use_beta_sigmas and not is_scipy_available():
             raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
@@ -259,8 +265,15 @@ def __init__(
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
     @property
-    def init_noise_sigma(self):
-        # standard deviation of the initial noise distribution
+    def init_noise_sigma(self) -> Union[float, torch.Tensor]:
+        """
+        The standard deviation of the initial noise distribution.
+
+        Returns:
+            `float` or `torch.Tensor`:
+                The standard deviation of the initial noise distribution, computed based on the maximum sigma value and
+                the timestep spacing configuration.
+        """
         max_sigma = max(self.sigmas) if isinstance(self.sigmas, list) else self.sigmas.max()
         if self.config.timestep_spacing in ["linspace", "trailing"]:
             return max_sigma
@@ -268,26 +281,34 @@ def init_noise_sigma(self):
         return (max_sigma**2 + 1) ** 0.5
 
     @property
-    def step_index(self):
+    def step_index(self) -> Optional[int]:
         """
-        The index counter for current timestep. It will increase 1 after each scheduler step.
+        The index counter for current timestep. It will increase by 1 after each scheduler step.
+        
+        Returns:
+            `int` or `None`:
+                The current step index, or `None` if not initialized.
         """
         return self._step_index
 
     @property
-    def begin_index(self):
+    def begin_index(self) -> Optional[int]:
         """
         The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
+        
+        Returns:
+            `int` or `None`:
+                The begin index for the scheduler, or `None` if not set.
         """
         return self._begin_index
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
-    def set_begin_index(self, begin_index: int = 0):
+    def set_begin_index(self, begin_index: int = 0) -> None:
         """
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -299,13 +320,13 @@ def scale_model_input(self, sample: torch.Tensor, timestep: Union[float, torch.T
 
         Args:
             sample (`torch.Tensor`):
-                The input sample.
-            timestep (`int`, *optional*):
+                The input sample to be scaled.
+            timestep (`float` or `torch.Tensor`):
                 The current timestep in the diffusion chain.
 
         Returns:
             `torch.Tensor`:
-                A scaled input sample.
+                A scaled input sample, divided by `(sigma**2 + 1) ** 0.5`.
         """
         if self.step_index is None:
             self._init_step_index(timestep)
@@ -318,17 +339,18 @@ def scale_model_input(self, sample: torch.Tensor, timestep: Union[float, torch.T
 
     def set_timesteps(
         self,
-        num_inference_steps: int = None,
-        device: Union[str, torch.device] = None,
+        num_inference_steps: Optional[int] = None,
+        device: Optional[Union[str, torch.device]] = None,
         timesteps: Optional[List[int]] = None,
         sigmas: Optional[List[float]] = None,
-    ):
+    ) -> None:
         """
         Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
         Args:
-            num_inference_steps (`int`):
-                The number of diffusion steps used when generating samples with a pre-trained model.
+            num_inference_steps (`int`, *optional*):
+                The number of diffusion steps used when generating samples with a pre-trained model. If `None`, 
+                `timesteps` or `sigmas` must be provided.
             device (`str` or `torch.device`, *optional*):
                 The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
             timesteps (`List[int]`, *optional*):
@@ -336,7 +358,7 @@ def set_timesteps(
                 based on the `timestep_spacing` attribute. If `timesteps` is passed, `num_inference_steps` and `sigmas`
                 must be `None`, and `timestep_spacing` attribute will be ignored.
             sigmas (`List[float]`, *optional*):
-                Custom sigmas used to support arbitrary timesteps schedule schedule. If `None`, timesteps and sigmas
+                Custom sigmas used to support arbitrary timesteps schedule. If `None`, timesteps and sigmas
                 will be generated based on the relevant scheduler attributes. If `sigmas` is passed,
                 `num_inference_steps` and `timesteps` must be `None`, and the timesteps will be generated based on the
                 custom sigmas schedule.
@@ -449,7 +471,20 @@ def set_timesteps(
         self._begin_index = None
         self.sigmas = sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
-    def _sigma_to_t(self, sigma, log_sigmas):
+    def _sigma_to_t(self, sigma: np.ndarray, log_sigmas: np.ndarray) -> np.ndarray:
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -473,8 +508,20 @@ def _sigma_to_t(self, sigma, log_sigmas):
         return t
 
     # Copied from https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
-    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -500,7 +547,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L26
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -523,7 +582,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et al.,
+        2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -551,7 +627,23 @@ def _convert_to_beta(
         )
         return sigmas
 
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if 
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -565,7 +657,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
 
         return indices[pos].item()
 
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -591,26 +690,33 @@ def step(
 
         Args:
             model_output (`torch.Tensor`):
-                The direct output from learned diffusion model.
-            timestep (`float`):
+                The direct output from the learned diffusion model.
+            timestep (`float` or `torch.Tensor`):
                 The current discrete timestep in the diffusion chain.
             sample (`torch.Tensor`):
                 A current instance of a sample created by the diffusion process.
-            s_churn (`float`):
-            s_tmin  (`float`):
-            s_tmax  (`float`):
-            s_noise (`float`, defaults to 1.0):
+            s_churn (`float`, *optional*, defaults to `0.0`):
+                Stochasticity parameter that controls the amount of noise added during sampling. Higher values increase
+                randomness.
+            s_tmin (`float`, *optional*, defaults to `0.0`):
+                Minimum timestep threshold for applying stochasticity. Only timesteps above this value will have noise
+                added.
+            s_tmax (`float`, *optional*, defaults to `inf`):
+                Maximum timestep threshold for applying stochasticity. Only timesteps below this value will have noise
+                added.
+            s_noise (`float`, *optional*, defaults to `1.0`):
                 Scaling factor for noise added to the sample.
             generator (`torch.Generator`, *optional*):
-                A random number generator.
-            return_dict (`bool`):
+                A random number generator for reproducible sampling.
+            return_dict (`bool`, *optional*, defaults to `True`):
                 Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
                 tuple.
 
         Returns:
             [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
-                If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
-                returned, otherwise a tuple is returned where the first element is the sample tensor.
+                If `return_dict` is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
+                returned, otherwise a tuple is returned where the first element is the sample tensor and the second 
+                element is the predicted original sample.
         """
 
         if isinstance(timestep, (int, torch.IntTensor, torch.LongTensor)):
@@ -689,6 +795,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
@@ -717,6 +838,24 @@ def add_noise(
         return noisy_samples
 
     def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: torch.Tensor) -> torch.Tensor:
+        """
+        Compute the velocity prediction for the given sample and noise at the specified timesteps.
+
+        This method implements the velocity prediction used in v-prediction models, which predicts a linear combination
+        of the sample and noise.
+
+        Args:
+            sample (`torch.Tensor`):
+                The input sample for which to compute the velocity.
+            noise (`torch.Tensor`):
+                The noise tensor corresponding to the sample.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to compute the velocity.
+
+        Returns:
+            `torch.Tensor`:
+                The velocity prediction computed as `sqrt(alpha_prod) * noise - sqrt(1 - alpha_prod) * sample`.
+        """
         if (
             isinstance(timesteps, int)
             or isinstance(timesteps, torch.IntTensor)
@@ -753,5 +892,5 @@ def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: tor
         velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
         return velocity
 
-    def __len__(self):
+    def __len__(self) -> int:
         return self.config.num_train_timesteps

From 8543b9ccbd1cc80dda1ed92cdf11497b67398b76 Mon Sep 17 00:00:00 2001
From: David El Malih <david@billiv.fr>
Date: Fri, 14 Nov 2025 00:46:42 +0100
Subject: [PATCH 2/3] refactor: enhance type hints and documentation across
 multiple schedulers

Updated type hints and improved docstrings in various scheduler classes, including CMStochasticIterativeScheduler, CosineDPMSolverMultistepScheduler, and others. This includes specifying parameter types, return types, and providing clearer descriptions of method functionalities. Notable changes include the addition of default values in the begin_index argument and enhanced explanations for noise addition methods. These improvements aim to enhance code clarity and maintainability across the scheduling module.
---
 .../scheduling_consistency_models.py          |  44 +++++++-
 .../scheduling_cosine_dpmsolver_multistep.py  |  30 ++++-
 src/diffusers/schedulers/scheduling_ddim.py   |   5 +-
 .../schedulers/scheduling_ddim_inverse.py     |   5 +-
 .../schedulers/scheduling_ddim_parallel.py    |   5 +-
 src/diffusers/schedulers/scheduling_ddpm.py   |   5 +-
 .../schedulers/scheduling_ddpm_parallel.py    |   5 +-
 .../schedulers/scheduling_deis_multistep.py   |  62 ++++++++++-
 .../scheduling_dpmsolver_multistep.py         |  67 ++++++++++-
 .../scheduling_dpmsolver_multistep_inverse.py |  60 +++++++++-
 .../schedulers/scheduling_dpmsolver_sde.py    |  90 ++++++++++++++-
 .../scheduling_dpmsolver_singlestep.py        |  62 ++++++++++-
 .../scheduling_edm_dpmsolver_multistep.py     |  30 ++++-
 .../schedulers/scheduling_edm_euler.py        |  44 +++++++-
 .../scheduling_euler_ancestral_discrete.py    |  49 ++++++++-
 .../schedulers/scheduling_euler_discrete.py   |  36 +++---
 .../scheduling_flow_match_euler_discrete.py   |  49 ++++++++-
 .../scheduling_flow_match_heun_discrete.py    |   2 +-
 .../schedulers/scheduling_flow_match_lcm.py   |  49 ++++++++-
 .../schedulers/scheduling_heun_discrete.py    | 104 +++++++++++++++++-
 src/diffusers/schedulers/scheduling_ipndm.py  |  29 ++++-
 .../scheduling_k_dpm_2_ancestral_discrete.py  | 104 +++++++++++++++++-
 .../schedulers/scheduling_k_dpm_2_discrete.py | 104 +++++++++++++++++-
 src/diffusers/schedulers/scheduling_lcm.py    |  34 +++++-
 .../schedulers/scheduling_lms_discrete.py     |  90 ++++++++++++++-
 .../schedulers/scheduling_sasolver.py         |  62 ++++++++++-
 src/diffusers/schedulers/scheduling_scm.py    |  29 ++++-
 src/diffusers/schedulers/scheduling_tcd.py    |  34 +++++-
 .../schedulers/scheduling_unipc_multistep.py  |  67 ++++++++++-
 29 files changed, 1236 insertions(+), 120 deletions(-)

diff --git a/src/diffusers/schedulers/scheduling_consistency_models.py b/src/diffusers/schedulers/scheduling_consistency_models.py
index 5d81d5eb8ac0..386a43db0f9c 100644
--- a/src/diffusers/schedulers/scheduling_consistency_models.py
+++ b/src/diffusers/schedulers/scheduling_consistency_models.py
@@ -121,7 +121,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -287,7 +287,23 @@ def get_scalings_for_boundary_condition(self, sigma):
         return c_skip, c_out
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -302,7 +318,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -410,6 +433,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_cosine_dpmsolver_multistep.py b/src/diffusers/schedulers/scheduling_cosine_dpmsolver_multistep.py
index b9567f2c47d5..7b11d704932b 100644
--- a/src/diffusers/schedulers/scheduling_cosine_dpmsolver_multistep.py
+++ b/src/diffusers/schedulers/scheduling_cosine_dpmsolver_multistep.py
@@ -137,7 +137,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -266,6 +266,19 @@ def _compute_exponential_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> t
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -537,6 +550,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_ddim.py b/src/diffusers/schedulers/scheduling_ddim.py
index 5ddc46ee4d2f..d7fe29a72ac9 100644
--- a/src/diffusers/schedulers/scheduling_ddim.py
+++ b/src/diffusers/schedulers/scheduling_ddim.py
@@ -99,10 +99,11 @@ def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
diff --git a/src/diffusers/schedulers/scheduling_ddim_inverse.py b/src/diffusers/schedulers/scheduling_ddim_inverse.py
index bed424e320be..a7717940e2a1 100644
--- a/src/diffusers/schedulers/scheduling_ddim_inverse.py
+++ b/src/diffusers/schedulers/scheduling_ddim_inverse.py
@@ -98,10 +98,11 @@ def rescale_zero_terminal_snr(betas):
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
diff --git a/src/diffusers/schedulers/scheduling_ddim_parallel.py b/src/diffusers/schedulers/scheduling_ddim_parallel.py
index 1432d835aea2..d957ade901b3 100644
--- a/src/diffusers/schedulers/scheduling_ddim_parallel.py
+++ b/src/diffusers/schedulers/scheduling_ddim_parallel.py
@@ -100,10 +100,11 @@ def rescale_zero_terminal_snr(betas):
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
diff --git a/src/diffusers/schedulers/scheduling_ddpm.py b/src/diffusers/schedulers/scheduling_ddpm.py
index 5ccf4adaebbc..1d0ad49c58cd 100644
--- a/src/diffusers/schedulers/scheduling_ddpm.py
+++ b/src/diffusers/schedulers/scheduling_ddpm.py
@@ -97,10 +97,11 @@ def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
diff --git a/src/diffusers/schedulers/scheduling_ddpm_parallel.py b/src/diffusers/schedulers/scheduling_ddpm_parallel.py
index 8740f14c66b4..78011d0e46a1 100644
--- a/src/diffusers/schedulers/scheduling_ddpm_parallel.py
+++ b/src/diffusers/schedulers/scheduling_ddpm_parallel.py
@@ -99,10 +99,11 @@ def rescale_zero_terminal_snr(betas):
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
diff --git a/src/diffusers/schedulers/scheduling_deis_multistep.py b/src/diffusers/schedulers/scheduling_deis_multistep.py
index 15d8a20e33b8..e87413985738 100644
--- a/src/diffusers/schedulers/scheduling_deis_multistep.py
+++ b/src/diffusers/schedulers/scheduling_deis_multistep.py
@@ -230,7 +230,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -364,6 +364,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -399,7 +412,19 @@ def _sigma_to_alpha_sigma_t(self, sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -425,7 +450,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -449,7 +486,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
index b1f218a5eb06..62915a713bc0 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
@@ -83,10 +83,11 @@ def rescale_zero_terminal_snr(betas):
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
@@ -323,7 +324,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -503,6 +504,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -537,7 +551,19 @@ def _sigma_to_alpha_sigma_t(self, sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -576,7 +602,19 @@ def _convert_to_lu(self, in_lambdas: torch.Tensor, num_inference_steps) -> torch
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -600,7 +638,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
index 476d2fc10568..d7894778e6f5 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
@@ -376,6 +376,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -411,7 +424,19 @@ def _sigma_to_alpha_sigma_t(self, sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -437,7 +462,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -461,7 +498,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_sde.py b/src/diffusers/schedulers/scheduling_dpmsolver_sde.py
index 2b02c2fd5e57..879fc9e767e8 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_sde.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_sde.py
@@ -251,7 +251,23 @@ def __init__(
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -266,7 +282,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -302,7 +325,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -430,6 +453,19 @@ def t_fn(_sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -468,7 +504,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -492,7 +540,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -646,6 +711,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py b/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
index e7fde2c2ba0d..cea5897e88f2 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
@@ -295,7 +295,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -454,6 +454,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -489,7 +502,19 @@ def _sigma_to_alpha_sigma_t(self, sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -515,7 +540,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -539,7 +576,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py b/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py
index f748c6c834a3..eeec588e27a3 100644
--- a/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py
+++ b/src/diffusers/schedulers/scheduling_edm_dpmsolver_multistep.py
@@ -169,7 +169,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -342,6 +342,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -682,6 +695,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_edm_euler.py b/src/diffusers/schedulers/scheduling_edm_euler.py
index dbeff3de5652..0bf17356a7fa 100644
--- a/src/diffusers/schedulers/scheduling_edm_euler.py
+++ b/src/diffusers/schedulers/scheduling_edm_euler.py
@@ -155,7 +155,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -284,7 +284,23 @@ def _compute_exponential_sigmas(self, ramp, sigma_min=None, sigma_max=None) -> t
         return sigmas
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -299,7 +315,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -413,6 +436,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py b/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py
index b2741c586be2..8f39507301ce 100644
--- a/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py
+++ b/src/diffusers/schedulers/scheduling_euler_ancestral_discrete.py
@@ -100,10 +100,11 @@ def rescale_zero_terminal_snr(betas):
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
@@ -245,7 +246,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -319,7 +320,23 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -334,7 +351,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -451,6 +475,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_euler_discrete.py b/src/diffusers/schedulers/scheduling_euler_discrete.py
index 0c732e7b515e..498c49d13988 100644
--- a/src/diffusers/schedulers/scheduling_euler_discrete.py
+++ b/src/diffusers/schedulers/scheduling_euler_discrete.py
@@ -103,10 +103,11 @@ def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
@@ -152,8 +153,8 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
         trained_betas (`np.ndarray`, *optional*):
             Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
         prediction_type (`Literal["epsilon", "sample", "v_prediction"]`, defaults to `"epsilon"`, *optional*):
-            Prediction type of the scheduler function; can be `"epsilon"` (predicts the noise of the diffusion process),
-            `"sample"` (directly predicts the noisy sample`) or `"v_prediction"` (see section 2.4 of [Imagen
+            Prediction type of the scheduler function; can be `"epsilon"` (predicts the noise of the diffusion
+            process), `"sample"` (directly predicts the noisy sample`) or `"v_prediction"` (see section 2.4 of [Imagen
             Video](https://imagen.research.google/video/paper.pdf) paper).
         interpolation_type (`Literal["linear", "log_linear"]`, defaults to `"linear"`, *optional*):
             The interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be one of
@@ -167,9 +168,11 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
             Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
             Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
         sigma_min (`float`, *optional*):
-            The minimum sigma value for the noise schedule. If not provided, defaults to the last sigma in the schedule.
+            The minimum sigma value for the noise schedule. If not provided, defaults to the last sigma in the
+            schedule.
         sigma_max (`float`, *optional*):
-            The maximum sigma value for the noise schedule. If not provided, defaults to the first sigma in the schedule.
+            The maximum sigma value for the noise schedule. If not provided, defaults to the first sigma in the
+            schedule.
         timestep_spacing (`Literal["linspace", "leading", "trailing"]`, defaults to `"linspace"`):
             The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
             Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
@@ -284,7 +287,7 @@ def init_noise_sigma(self) -> Union[float, torch.Tensor]:
     def step_index(self) -> Optional[int]:
         """
         The index counter for current timestep. It will increase by 1 after each scheduler step.
-        
+
         Returns:
             `int` or `None`:
                 The current step index, or `None` if not initialized.
@@ -295,7 +298,7 @@ def step_index(self) -> Optional[int]:
     def begin_index(self) -> Optional[int]:
         """
         The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
-        
+
         Returns:
             `int` or `None`:
                 The begin index for the scheduler, or `None` if not set.
@@ -349,7 +352,7 @@ def set_timesteps(
 
         Args:
             num_inference_steps (`int`, *optional*):
-                The number of diffusion steps used when generating samples with a pre-trained model. If `None`, 
+                The number of diffusion steps used when generating samples with a pre-trained model. If `None`,
                 `timesteps` or `sigmas` must be provided.
             device (`str` or `torch.device`, *optional*):
                 The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
@@ -358,10 +361,9 @@ def set_timesteps(
                 based on the `timestep_spacing` attribute. If `timesteps` is passed, `num_inference_steps` and `sigmas`
                 must be `None`, and `timestep_spacing` attribute will be ignored.
             sigmas (`List[float]`, *optional*):
-                Custom sigmas used to support arbitrary timesteps schedule. If `None`, timesteps and sigmas
-                will be generated based on the relevant scheduler attributes. If `sigmas` is passed,
-                `num_inference_steps` and `timesteps` must be `None`, and the timesteps will be generated based on the
-                custom sigmas schedule.
+                Custom sigmas used to support arbitrary timesteps schedule. If `None`, timesteps and sigmas will be
+                generated based on the relevant scheduler attributes. If `sigmas` is passed, `num_inference_steps` and
+                `timesteps` must be `None`, and the timesteps will be generated based on the custom sigmas schedule.
         """
 
         if timesteps is not None and sigmas is not None:
@@ -583,8 +585,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et al.,
-        2024).
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -641,7 +643,7 @@ def index_for_timestep(
 
         Returns:
             `int`:
-                The index of the timestep in the schedule. For the very first step, returns the second index if 
+                The index of the timestep in the schedule. For the very first step, returns the second index if
                 multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
         """
         if schedule_timesteps is None:
@@ -715,7 +717,7 @@ def step(
         Returns:
             [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
                 If `return_dict` is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
-                returned, otherwise a tuple is returned where the first element is the sample tensor and the second 
+                returned, otherwise a tuple is returned where the first element is the sample tensor and the second
                 element is the predicted original sample.
         """
 
diff --git a/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py b/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
index 1a4f12ddfa53..3598a8d57d8c 100644
--- a/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
+++ b/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
@@ -160,7 +160,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -473,7 +473,19 @@ def step(
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -499,7 +511,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -523,7 +547,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_flow_match_heun_discrete.py b/src/diffusers/schedulers/scheduling_flow_match_heun_discrete.py
index 38e5f1ba77a8..6febee444c5a 100644
--- a/src/diffusers/schedulers/scheduling_flow_match_heun_discrete.py
+++ b/src/diffusers/schedulers/scheduling_flow_match_heun_discrete.py
@@ -102,7 +102,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
diff --git a/src/diffusers/schedulers/scheduling_flow_match_lcm.py b/src/diffusers/schedulers/scheduling_flow_match_lcm.py
index 933bb1cf8e3d..910df7371c3f 100644
--- a/src/diffusers/schedulers/scheduling_flow_match_lcm.py
+++ b/src/diffusers/schedulers/scheduling_flow_match_lcm.py
@@ -168,7 +168,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -473,7 +473,19 @@ def step(
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -499,7 +511,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -523,7 +547,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_heun_discrete.py b/src/diffusers/schedulers/scheduling_heun_discrete.py
index db81fc82bcf3..5c41231e8f49 100644
--- a/src/diffusers/schedulers/scheduling_heun_discrete.py
+++ b/src/diffusers/schedulers/scheduling_heun_discrete.py
@@ -188,7 +188,23 @@ def __init__(
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -230,7 +246,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -355,6 +371,19 @@ def set_timesteps(
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -379,7 +408,19 @@ def _sigma_to_t(self, sigma, log_sigmas):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -405,7 +446,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -429,7 +482,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -462,7 +532,14 @@ def state_in_first_order(self):
         return self.dt is None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -580,6 +657,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_ipndm.py b/src/diffusers/schedulers/scheduling_ipndm.py
index 23bc21f10ca4..da188fe8297c 100644
--- a/src/diffusers/schedulers/scheduling_ipndm.py
+++ b/src/diffusers/schedulers/scheduling_ipndm.py
@@ -78,7 +78,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -112,7 +112,23 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
         self._begin_index = None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -127,7 +143,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
diff --git a/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py b/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py
index 48cc01e6aac7..510761350981 100644
--- a/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py
+++ b/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py
@@ -207,7 +207,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -343,6 +343,19 @@ def set_timesteps(
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -367,7 +380,19 @@ def _sigma_to_t(self, sigma, log_sigmas):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -393,7 +418,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -417,7 +454,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -450,7 +504,23 @@ def state_in_first_order(self):
         return self.sample is None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -465,7 +535,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -587,6 +664,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py b/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py
index aaf6a48b57be..aeae14b5ef58 100644
--- a/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py
+++ b/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py
@@ -207,7 +207,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -331,7 +331,23 @@ def state_in_first_order(self):
         return self.sample is None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -346,7 +362,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -356,6 +379,19 @@ def _init_step_index(self, timestep):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -380,7 +416,19 @@ def _sigma_to_t(self, sigma, log_sigmas):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -406,7 +454,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -430,7 +490,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -559,6 +636,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_lcm.py b/src/diffusers/schedulers/scheduling_lcm.py
index 36587537ec1b..a7b0644de4f5 100644
--- a/src/diffusers/schedulers/scheduling_lcm.py
+++ b/src/diffusers/schedulers/scheduling_lcm.py
@@ -102,10 +102,11 @@ def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
@@ -251,7 +252,23 @@ def __init__(
         self._begin_index = None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -266,7 +283,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -291,7 +315,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
diff --git a/src/diffusers/schedulers/scheduling_lms_discrete.py b/src/diffusers/schedulers/scheduling_lms_discrete.py
index 6fa9c2f7fbcf..38806a0e8884 100644
--- a/src/diffusers/schedulers/scheduling_lms_discrete.py
+++ b/src/diffusers/schedulers/scheduling_lms_discrete.py
@@ -210,7 +210,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -320,7 +320,23 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
         self.derivatives = []
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -335,7 +351,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -345,6 +368,19 @@ def _init_step_index(self, timestep):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -383,7 +419,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -407,7 +455,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -522,6 +587,21 @@ def add_noise(
         noise: torch.Tensor,
         timesteps: torch.Tensor,
     ) -> torch.Tensor:
+        """
+        Add noise to the original samples according to the noise schedule at the specified timesteps.
+
+        Args:
+            original_samples (`torch.Tensor`):
+                The original samples to which noise will be added.
+            noise (`torch.Tensor`):
+                The noise tensor to add to the original samples.
+            timesteps (`torch.Tensor`):
+                The timesteps at which to add noise, determining the noise level from the schedule.
+
+        Returns:
+            `torch.Tensor`:
+                The noisy samples with added noise scaled according to the timestep schedule.
+        """
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
         if original_samples.device.type == "mps" and torch.is_floating_point(timesteps):
diff --git a/src/diffusers/schedulers/scheduling_sasolver.py b/src/diffusers/schedulers/scheduling_sasolver.py
index 30a3eb294a04..05a8bdc5ad6b 100644
--- a/src/diffusers/schedulers/scheduling_sasolver.py
+++ b/src/diffusers/schedulers/scheduling_sasolver.py
@@ -254,7 +254,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -386,6 +386,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -421,7 +434,19 @@ def _sigma_to_alpha_sigma_t(self, sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -447,7 +472,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -471,7 +508,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
diff --git a/src/diffusers/schedulers/scheduling_scm.py b/src/diffusers/schedulers/scheduling_scm.py
index 63b4a109ff9b..7b01d886299c 100644
--- a/src/diffusers/schedulers/scheduling_scm.py
+++ b/src/diffusers/schedulers/scheduling_scm.py
@@ -109,7 +109,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -173,7 +173,14 @@ def set_timesteps(
         self._begin_index = None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -182,7 +189,23 @@ def _init_step_index(self, timestep):
             self._step_index = self._begin_index
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
diff --git a/src/diffusers/schedulers/scheduling_tcd.py b/src/diffusers/schedulers/scheduling_tcd.py
index 101b1569a145..37b41c87f8a2 100644
--- a/src/diffusers/schedulers/scheduling_tcd.py
+++ b/src/diffusers/schedulers/scheduling_tcd.py
@@ -101,10 +101,11 @@ def rescale_zero_terminal_snr(betas: torch.Tensor) -> torch.Tensor:
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
@@ -252,7 +253,23 @@ def __init__(
         self._begin_index = None
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep
-    def index_for_timestep(self, timestep, schedule_timesteps=None):
+    def index_for_timestep(
+        self, timestep: Union[float, torch.Tensor], schedule_timesteps: Optional[torch.Tensor] = None
+    ) -> int:
+        """
+        Find the index of a given timestep in the timestep schedule.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The timestep value to find in the schedule.
+            schedule_timesteps (`torch.Tensor`, *optional*):
+                The timestep schedule to search in. If `None`, uses `self.timesteps`.
+
+        Returns:
+            `int`:
+                The index of the timestep in the schedule. For the very first step, returns the second index if
+                multiple matches exist to avoid skipping a sigma when starting mid-schedule (e.g., for image-to-image).
+        """
         if schedule_timesteps is None:
             schedule_timesteps = self.timesteps
 
@@ -267,7 +284,14 @@ def index_for_timestep(self, timestep, schedule_timesteps=None):
         return indices[pos].item()
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[float, torch.Tensor]) -> None:
+        """
+        Initialize the step index for the scheduler based on the given timestep.
+
+        Args:
+            timestep (`float` or `torch.Tensor`):
+                The current timestep to initialize the step index from.
+        """
         if self.begin_index is None:
             if isinstance(timestep, torch.Tensor):
                 timestep = timestep.to(self.timesteps.device)
@@ -292,7 +316,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
diff --git a/src/diffusers/schedulers/scheduling_unipc_multistep.py b/src/diffusers/schedulers/scheduling_unipc_multistep.py
index d985871df109..a36aea3bc349 100644
--- a/src/diffusers/schedulers/scheduling_unipc_multistep.py
+++ b/src/diffusers/schedulers/scheduling_unipc_multistep.py
@@ -83,10 +83,11 @@ def rescale_zero_terminal_snr(betas):
 
     Args:
         betas (`torch.Tensor`):
-            the betas that the scheduler is being initialized with.
+            The betas that the scheduler is being initialized with.
 
     Returns:
-        `torch.Tensor`: rescaled betas with zero terminal SNR
+        `torch.Tensor`:
+            Rescaled betas with zero terminal SNR.
     """
     # Convert betas to alphas_bar_sqrt
     alphas = 1.0 - betas
@@ -297,7 +298,7 @@ def set_begin_index(self, begin_index: int = 0):
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
         Args:
-            begin_index (`int`):
+            begin_index (`int`, defaults to `0`):
                 The begin index for the scheduler.
         """
         self._begin_index = begin_index
@@ -475,6 +476,19 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
     def _sigma_to_t(self, sigma, log_sigmas):
+        """
+        Convert sigma values to corresponding timestep values through interpolation.
+
+        Args:
+            sigma (`np.ndarray`):
+                The sigma value(s) to convert to timestep(s).
+            log_sigmas (`np.ndarray`):
+                The logarithm of the sigma schedule used for interpolation.
+
+        Returns:
+            `np.ndarray`:
+                The interpolated timestep value(s) corresponding to the input sigma(s).
+        """
         # get log sigma
         log_sigma = np.log(np.maximum(sigma, 1e-10))
 
@@ -510,7 +524,19 @@ def _sigma_to_alpha_sigma_t(self, sigma):
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
-        """Constructs the noise schedule of Karras et al. (2022)."""
+        """
+        Construct the noise schedule of Karras et al. (2022).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following the Karras noise schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -536,7 +562,19 @@ def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> to
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential
     def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
-        """Constructs an exponential noise schedule."""
+        """
+        Construct an exponential noise schedule.
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following an exponential schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers
@@ -560,7 +598,24 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
     def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
-        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+        """
+        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
+        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+
+        Args:
+            in_sigmas (`torch.Tensor`):
+                The input sigma values to be converted.
+            num_inference_steps (`int`):
+                The number of inference steps to generate the noise schedule for.
+            alpha (`float`, *optional*, defaults to `0.6`):
+                The alpha parameter for the beta distribution.
+            beta (`float`, *optional*, defaults to `0.6`):
+                The beta parameter for the beta distribution.
+
+        Returns:
+            `torch.Tensor`:
+                The converted sigma values following a beta distribution schedule.
+        """
 
         # Hack to make sure that other schedulers which copy this function don't break
         # TODO: Add this logic to the other schedulers

From 387f89ccb5b9b123adc86458857345596d13344a Mon Sep 17 00:00:00 2001
From: David El Malih <david@billiv.fr>
Date: Fri, 14 Nov 2025 19:22:49 +0100
Subject: [PATCH 3/3] refactor: update docstrings to clarify noise schedule
 construction

Revised docstrings across multiple scheduler classes to enhance clarity regarding the construction of noise schedules. Updated references to relevant papers, ensuring accurate citations for the methodologies used. This includes changes in DEISMultistepScheduler, DPMSolverMultistepInverseScheduler, and others, improving documentation consistency and readability.
---
 src/diffusers/schedulers/scheduling_deis_multistep.py      | 7 ++++---
 src/diffusers/schedulers/scheduling_dpmsolver_multistep.py | 7 ++++---
 .../schedulers/scheduling_dpmsolver_multistep_inverse.py   | 7 ++++---
 src/diffusers/schedulers/scheduling_dpmsolver_sde.py       | 4 ++--
 .../schedulers/scheduling_dpmsolver_singlestep.py          | 7 ++++---
 src/diffusers/schedulers/scheduling_euler_discrete.py      | 7 ++++---
 .../schedulers/scheduling_flow_match_euler_discrete.py     | 7 ++++---
 src/diffusers/schedulers/scheduling_flow_match_lcm.py      | 7 ++++---
 src/diffusers/schedulers/scheduling_heun_discrete.py       | 7 ++++---
 .../schedulers/scheduling_k_dpm_2_ancestral_discrete.py    | 7 ++++---
 src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py    | 7 ++++---
 src/diffusers/schedulers/scheduling_lms_discrete.py        | 4 ++--
 src/diffusers/schedulers/scheduling_sasolver.py            | 7 ++++---
 src/diffusers/schedulers/scheduling_unipc_multistep.py     | 7 ++++---
 14 files changed, 52 insertions(+), 40 deletions(-)

diff --git a/src/diffusers/schedulers/scheduling_deis_multistep.py b/src/diffusers/schedulers/scheduling_deis_multistep.py
index e87413985738..bf8e1d98d6c0 100644
--- a/src/diffusers/schedulers/scheduling_deis_multistep.py
+++ b/src/diffusers/schedulers/scheduling_deis_multistep.py
@@ -413,7 +413,8 @@ def _sigma_to_alpha_sigma_t(self, sigma):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -487,8 +488,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
index 62915a713bc0..dee97f39ff68 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
@@ -552,7 +552,8 @@ def _sigma_to_alpha_sigma_t(self, sigma):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -639,8 +640,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
index d7894778e6f5..0f734aeb54c9 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
@@ -425,7 +425,8 @@ def _sigma_to_alpha_sigma_t(self, sigma):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -499,8 +500,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_sde.py b/src/diffusers/schedulers/scheduling_dpmsolver_sde.py
index 879fc9e767e8..e22954d4e6ea 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_sde.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_sde.py
@@ -541,8 +541,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py b/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
index cea5897e88f2..0b271d7eacb4 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
@@ -503,7 +503,8 @@ def _sigma_to_alpha_sigma_t(self, sigma):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -577,8 +578,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_euler_discrete.py b/src/diffusers/schedulers/scheduling_euler_discrete.py
index 498c49d13988..5ea926c4ca38 100644
--- a/src/diffusers/schedulers/scheduling_euler_discrete.py
+++ b/src/diffusers/schedulers/scheduling_euler_discrete.py
@@ -512,7 +512,8 @@ def _sigma_to_t(self, sigma: np.ndarray, log_sigmas: np.ndarray) -> np.ndarray:
     # Copied from https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -585,8 +586,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py b/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
index 3598a8d57d8c..9fd61d9e18d1 100644
--- a/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
+++ b/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
@@ -474,7 +474,8 @@ def step(
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -548,8 +549,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_flow_match_lcm.py b/src/diffusers/schedulers/scheduling_flow_match_lcm.py
index 910df7371c3f..25186d1fe969 100644
--- a/src/diffusers/schedulers/scheduling_flow_match_lcm.py
+++ b/src/diffusers/schedulers/scheduling_flow_match_lcm.py
@@ -474,7 +474,8 @@ def step(
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -548,8 +549,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_heun_discrete.py b/src/diffusers/schedulers/scheduling_heun_discrete.py
index 5c41231e8f49..930b0344646d 100644
--- a/src/diffusers/schedulers/scheduling_heun_discrete.py
+++ b/src/diffusers/schedulers/scheduling_heun_discrete.py
@@ -409,7 +409,8 @@ def _sigma_to_t(self, sigma, log_sigmas):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -483,8 +484,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py b/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py
index 510761350981..595b93c39d4c 100644
--- a/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py
+++ b/src/diffusers/schedulers/scheduling_k_dpm_2_ancestral_discrete.py
@@ -381,7 +381,8 @@ def _sigma_to_t(self, sigma, log_sigmas):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -455,8 +456,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py b/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py
index aeae14b5ef58..7db12227229e 100644
--- a/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py
+++ b/src/diffusers/schedulers/scheduling_k_dpm_2_discrete.py
@@ -417,7 +417,8 @@ def _sigma_to_t(self, sigma, log_sigmas):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -491,8 +492,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_lms_discrete.py b/src/diffusers/schedulers/scheduling_lms_discrete.py
index 38806a0e8884..573678b100ba 100644
--- a/src/diffusers/schedulers/scheduling_lms_discrete.py
+++ b/src/diffusers/schedulers/scheduling_lms_discrete.py
@@ -456,8 +456,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_sasolver.py b/src/diffusers/schedulers/scheduling_sasolver.py
index 05a8bdc5ad6b..d9054c39c9de 100644
--- a/src/diffusers/schedulers/scheduling_sasolver.py
+++ b/src/diffusers/schedulers/scheduling_sasolver.py
@@ -435,7 +435,8 @@ def _sigma_to_alpha_sigma_t(self, sigma):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -509,8 +510,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):
diff --git a/src/diffusers/schedulers/scheduling_unipc_multistep.py b/src/diffusers/schedulers/scheduling_unipc_multistep.py
index a36aea3bc349..7dc5f467680b 100644
--- a/src/diffusers/schedulers/scheduling_unipc_multistep.py
+++ b/src/diffusers/schedulers/scheduling_unipc_multistep.py
@@ -525,7 +525,8 @@ def _sigma_to_alpha_sigma_t(self, sigma):
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
     def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
         """
-        Construct the noise schedule of Karras et al. (2022).
+        Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
+        Models](https://huggingface.co/papers/2206.00364).
 
         Args:
             in_sigmas (`torch.Tensor`):
@@ -599,8 +600,8 @@ def _convert_to_beta(
         self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
     ) -> torch.Tensor:
         """
-        Construct a beta noise schedule as proposed in ["Beta Sampling is All You
-        Need"](https://huggingface.co/papers/2407.12173) (Lee et al., 2024).
+        Construct a beta noise schedule as proposed in [Beta Sampling is All You
+        Need](https://huggingface.co/papers/2407.12173).
 
         Args:
             in_sigmas (`torch.Tensor`):