arcDiff

Improving Denoising Diffusion Models via Simultaneous Estimation of Image and Noise

Official implementation of arcDiff, a faster and higher-quality inverse diffusion method via:

1. Arc reparameterization of the diffusion trajectory, and
2. Dual estimation of both clean image and noise.

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Overview

This repository implements two key contributions that improve denoising diffusion models:

Overview of arcDiff: (left) Diffusion process reparameterized on a quarter-circular arc between image $x_0$ and noise $\epsilon$; (right) U-Net simultaneously estimating both clean image $\hat{x}_0$ and noise $\hat{\epsilon}$ from noisy input $x_t$.

1. Arc Reparameterization

We reparameterize the diffusion process using the angle η on a quarter-circular arc between the image and noise:

$$\sqrt{\bar{\alpha}} = \cos(\eta)$$

This formulation:

• Eliminates two singularities in the standard diffusion formulation
• Expresses diffusion evolution as a well-behaved ODE (ordinary differential equation)
• Enables effective use of higher-order ODE solvers such as Runge-Kutta methods for faster sampling

2. Dual Estimation (Image + Noise)

Our network simultaneously estimates both:

• Image (x₀) — the clean image
• Noise (ε) — the noise component

Accurate estimation of both quantities is crucial at different stages of the inverse diffusion process. This dual estimation enables more stable calculations of the update step during sampling.

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Results

Together, these improvements lead to:

• Faster generation — ability to converge on high-quality images more quickly
• Higher quality — as measured by:
  • Fréchet Inception Distance (FID)
  • Spatial Fréchet Inception Distance (sFID)
  • Precision
  • Recall

CIFAR-10

CelebA

LSUN Church

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Paper & Citation

If you find this work useful, please cite:

@article{zhang2023improving,
  title={Improving Denoising Diffusion Models via Simultaneous Estimation of Image and Noise},
  author={Zhang, Zhenkai and Ehinger, Krista A and Drummond, Tom},
  journal={arXiv preprint arXiv:2310.17167},
  year={2023}
}

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Installation

# Clone the repository
git clone https://github.com/your-org/arcDiff.git
cd arcDiff

# Install dependencies (coming soon)
pip install -r requirements.txt

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Usage

(Usage instructions will be added as the codebase is developed.)

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License

This project is licensed under the Apache License 2.0 — see the LICENSE file for details.

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Acknowledgements

This implementation is based on the DDIM codebase (Song et al., Denoising Diffusion Implicit Models, ICLR 2021).