Azula - Diffusion models in PyTorch

Azula is a Python package that implements diffusion models in PyTorch. Its goal is to unify the different formalisms and notations of the generative diffusion models literature into a single, convenient and hackable interface.

In the Avatar cartoon, Azula is a powerful fire and lightning bender ⚡️

Installation

The azula package is available on PyPI, which means it is installable via pip.

pip install azula

Alternatively, if you need the latest features, you can install it from the repository.

pip install git+https://github.com/probabilists/azula

Getting started

In Azula's formalism, a diffusion model is the composition of three elements: a noise schedule, a denoiser and a sampler.

• A noise schedule is a mapping from a time $t \in [0, 1]$ to the signal scale $\alpha_t$ and the noise scale $\sigma_t$ in a perturbation kernel $p(X_t \mid X) = \mathcal{N}(X_t \mid \alpha_t X_t, \sigma_t^2 I)$ from a "clean" random variable $X \sim p(X)$ to a "noisy" random variable $X_t$.

• A denoiser is a neural network trained to predict $X$ given $X_t$.

• A sampler defines a series of transition kernels $q(X_s \mid X_t)$ from $t$ to $s < t$ based on a noise schedule and a denoiser. Simulating these transitions from $t = 1$ to $0$ samples approximately from $p(X)$.

This formalism is closely followed by Azula's API.

from azula.denoise import PreconditionedDenoiser
from azula.noise import VPSchedule
from azula.sample import DDPMSampler

# Choose the variance preserving (VP) noise schedule
schedule = VPSchedule()

# Initialize a denoiser
denoiser = PreconditionedDenoiser(
    backbone=CustomNN(in_features=5, out_features=5),
    schedule=schedule,
)

# Train to predict x given x_t
optimizer = torch.optim.Adam(denoiser.parameters(), lr=1e-3)

for x in train_loader:
    t = torch.rand((batch_size,))

    loss = denoiser.loss(x, t).mean()
    loss.backward()

    optimizer.step()
    optimizer.zero_grad()

# Generate 64 points in 1000 steps
sampler = DDPMSampler(denoiser.eval(), steps=1000)

x1 = sampler.init((64, 5))
x0 = sampler(x1)

Alternatively, Azula's plugin interface allows to load pre-trained models and use them with the same convenient interface.

import sys

sys.path.append("path/to/guided-diffusion")

from azula.plugins import adm
from azula.sample import DDIMSampler

# Download weights from openai/guided-diffusion
denoiser = adm.load_model("imagenet_256x256")

# Generate a batch of 4 images
sampler = DDIMSampler(denoiser, steps=64).cuda()

x1 = sampler.init((4, 3 * 256 * 256))
x0 = sampler(x1)

images = torch.clip((x0 + 1) / 2, min=0, max=1).reshape(4, 3, 256, 256)

For more information, check out the documentation and tutorials at azula.readthedocs.io.

Contributing

If you have a question, an issue or would like to contribute, please read our contributing guidelines.