diff --git a/src/diffusers/schedulers/scheduling_unipc_multistep.py b/src/diffusers/schedulers/scheduling_unipc_multistep.py
index 6800c1220177..689c6a06350b 100644
--- a/src/diffusers/schedulers/scheduling_unipc_multistep.py
+++ b/src/diffusers/schedulers/scheduling_unipc_multistep.py
@@ -77,7 +77,7 @@ 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)
 
@@ -127,19 +127,19 @@ class UniPCMultistepScheduler(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 (`"linear"`, `"scaled_linear"`, or `"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`, `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`.
-        solver_order (`int`, default `2`):
+        solver_order (`int`, defaults to `2`):
             The UniPC order which can be any positive integer. The effective order of accuracy is `solver_order + 1`
             due to the UniC. It is recommended to use `solver_order=2` for guided sampling, and `solver_order=3` for
             unconditional sampling.
-        prediction_type (`str`, defaults to `epsilon`, *optional*):
+        prediction_type (`"epsilon"`, `"sample"`, `"v_prediction"`, or `"flow_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://huggingface.co/papers/2210.02303) paper).
+            `sample` (directly predicts the noisy sample`), `v_prediction` (see section 2.4 of [Imagen
+            Video](https://huggingface.co/papers/2210.02303) paper), or `flow_prediction`.
         thresholding (`bool`, defaults to `False`):
             Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
             as Stable Diffusion.
@@ -149,7 +149,7 @@ class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
             The threshold value for dynamic thresholding. Valid only when `thresholding=True` and `predict_x0=True`.
         predict_x0 (`bool`, defaults to `True`):
             Whether to use the updating algorithm on the predicted x0.
-        solver_type (`str`, default `bh2`):
+        solver_type (`"bh1"` or `"bh2"`, defaults to `"bh2"`):
             Solver type for UniPC. It is recommended to use `bh1` for unconditional sampling when steps < 10, and `bh2`
             otherwise.
         lower_order_final (`bool`, default `True`):
@@ -171,12 +171,12 @@ class UniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
             Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
         use_flow_sigmas (`bool`, *optional*, defaults to `False`):
             Whether to use flow sigmas for step sizes in the noise schedule during the sampling process.
-        timestep_spacing (`str`, defaults to `"linspace"`):
+        timestep_spacing (`"linspace"`, `"leading"`, or `"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.
         steps_offset (`int`, defaults to 0):
             An offset added to the inference steps, as required by some model families.
-        final_sigmas_type (`str`, defaults to `"zero"`):
+        final_sigmas_type (`"zero"` or `"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.
         rescale_betas_zero_snr (`bool`, defaults to `False`):
@@ -194,30 +194,30 @@ 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,
         solver_order: int = 2,
-        prediction_type: str = "epsilon",
+        prediction_type: Literal["epsilon", "sample", "v_prediction", "flow_prediction"] = "epsilon",
         thresholding: bool = False,
         dynamic_thresholding_ratio: float = 0.995,
         sample_max_value: float = 1.0,
         predict_x0: bool = True,
-        solver_type: str = "bh2",
+        solver_type: Literal["bh1", "bh2"] = "bh2",
         lower_order_final: bool = True,
         disable_corrector: List[int] = [],
-        solver_p: SchedulerMixin = None,
+        solver_p: Optional[SchedulerMixin] = None,
         use_karras_sigmas: Optional[bool] = False,
         use_exponential_sigmas: Optional[bool] = False,
         use_beta_sigmas: Optional[bool] = False,
         use_flow_sigmas: Optional[bool] = False,
         flow_shift: Optional[float] = 1.0,
-        timestep_spacing: str = "linspace",
+        timestep_spacing: Literal["linspace", "leading", "trailing"] = "linspace",
         steps_offset: int = 0,
-        final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
+        final_sigmas_type: Optional[Literal["zero", "sigma_min"]] = "zero",
         rescale_betas_zero_snr: bool = False,
         use_dynamic_shifting: bool = False,
-        time_shift_type: str = "exponential",
-    ):
+        time_shift_type: Literal["exponential"] = "exponential",
+    ) -> None:
         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.")
         if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
@@ -279,21 +279,21 @@ def __init__(
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
     @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.
         """
         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.
         """
         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.
 
@@ -304,8 +304,8 @@ def set_begin_index(self, begin_index: int = 0):
         self._begin_index = begin_index
 
     def set_timesteps(
-        self, num_inference_steps: int, device: Union[str, torch.device] = None, mu: Optional[float] = None
-    ):
+        self, num_inference_steps: int, device: Optional[Union[str, torch.device]] = None, mu: Optional[float] = None
+    ) -> None:
         """
         Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
@@ -314,6 +314,8 @@ def set_timesteps(
                 The number of diffusion steps used when generating samples with a pre-trained model.
             device (`str` or `torch.device`, *optional*):
                 The device to which the timesteps should be moved to. If `None`, the timesteps are not moved.
+            mu (`float`, *optional*):
+                Optional mu parameter for dynamic shifting when using exponential time shift type.
         """
         # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://huggingface.co/papers/2305.08891
         if mu is not None:
@@ -475,7 +477,7 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
         return sample
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
-    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.
 
@@ -512,7 +514,7 @@ def _sigma_to_t(self, sigma, log_sigmas):
         return t
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t
-    def _sigma_to_alpha_sigma_t(self, sigma):
+    def _sigma_to_alpha_sigma_t(self, sigma: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
         """
         Convert sigma values to alpha_t and sigma_t values.
 
@@ -534,7 +536,7 @@ def _sigma_to_alpha_sigma_t(self, sigma):
         return alpha_t, sigma_t
 
     # 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:
+    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
         """
         Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
         Models](https://huggingface.co/papers/2206.00364).
@@ -1030,7 +1032,7 @@ def index_for_timestep(
         return step_index
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[int, torch.Tensor]) -> None:
         """
         Initialize the step_index counter for the scheduler.
 
@@ -1060,11 +1062,11 @@ def step(
         Args:
             model_output (`torch.Tensor`):
                 The direct output from learned diffusion model.
-            timestep (`int`):
+            timestep (`int` 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.
-            return_dict (`bool`):
+            return_dict (`bool`, defaults to `True`):
                 Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
 
         Returns:
@@ -1192,5 +1194,5 @@ def add_noise(
         noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
-    def __len__(self):
+    def __len__(self) -> int:
         return self.config.num_train_timesteps