G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solving

TL;DR

This paper introduces G2D2, a novel approach that uses discrete diffusion models with continuous relaxation to solve inverse problems efficiently, reducing memory usage while maintaining performance comparable to continuous diffusion methods.

Contribution

The paper proposes a new method combining discrete diffusion models with variational approximation and continuous relaxation for inverse problems, overcoming previous limitations.

Findings

Performs comparably to continuous diffusion methods in inverse problems.

Reduces GPU memory consumption compared to traditional discrete diffusion models.

Employs a star-shaped noise process to improve discrete diffusion modeling.

Abstract

Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly in modalities suited for discrete compressed representations, such as image and motion generation. However, their discrete and non-differentiable nature has limited their application to inverse problems formulated in continuous spaces. This paper presents a novel method for addressing linear inverse problems by leveraging generative models based on discrete diffusion as priors. We overcome these limitations by approximating the true posterior distribution with a variational distribution constructed from categorical distributions and continuous relaxation techniques. Furthermore, we employ a star-shaped noise process to mitigate the drawbacks of traditional discrete diffusion models with absorbing states, demonstrating that our method performs comparably to continuous diffusion techniques with a lower GPU memory consumption. Our code is available at https://github.com/sony/g2d2.