Exponential Residual Flows: An ODE-Based Sampler for Discrete Diffusion Models

Forum topic · 小凯 · 2026-10-30

Summary

A forum post on zhichai.net introduces the arXiv paper 2610.40618, "An ODE-based Sampler for Discrete Diffusion Models" by Samson Gourevitch, Yazid Janati, Eric Moulines, Eric P. Xing, Alain Durmus, and Giacomo Zanella. Continuous diffusion models admit a deterministic probability flow ODE that reproduces their marginals, enabling accelerated sampling and consistency distillation. This paper asks whether an analogous formulation exists for discrete diffusion models and answers affirmatively by introducing exponential residual flows (ERFs). The framework augments each token and position of the discrete state with a continuous residual variable. These residuals evolve deterministically under piecewise-defined ODEs whose vector fields depend on the current discrete state and the forward and backward rate matrices of the prescribed diffusion model. The discrete state changes whenever a residual reaches a threshold, yielding a deterministic sampler that exactly reproduces the discrete diffusion model's marginals. This bridges deterministic ODE sampling from continuous to discrete diffusion, opening the door to accelerated sampling and distillation techniques for discrete-state generative models.

Paper Overview

Research area: Machine Learning Authors: Samson Gourevitch, Yazid Janati, Eric Moulines, Eric P. Xing, Alain Durmus, Giacomo Zanella arXiv: 2610.40618

> Note: the Chinese summary attached to the original forum post appears to describe an unrelated paper (WxCrop, an agricultural weather-risk agent) and does not match the arXiv ID listed. The content below is based on the paper's original abstract.

Original Abstract (excerpt)

The marginals of a continuous diffusion model can be reproduced by a deterministic ordinary differential equation (ODE), known as the probability flow ODE, which provides a foundation for accelerated sampling and consistency distillation. In this paper we address the question whether an analogous formulation exists for discrete diffusion models and answer it affirmatively by introducing exponential residual flows (ERFs).

Our framework augments the discrete state with a continuous residual variable for each token and position. These residuals evolve deterministically according to piecewise-defined ODEs whose vector fields depend on the current discrete state and the forward and backward rate matrices of the prescribed diffusion model. The discrete state changes whenever a residual reaches a threshold.

Why It Matters

Extends the probability flow ODE concept from continuous to discrete diffusion models.
The resulting deterministic sampler exactly reproduces the marginals of the underlying discrete diffusion process.
Provides a foundation for potential accelerated sampling and consistency distillation in discrete-state generative models (e.g., text and other token-based data).

*Auto-collected on 2026-10-31.*