Exponential Residual Flows: an ODE sampler for discrete diffusion models
_onionesque · x · 2026-10-31
A new arXiv paper (Oct 29, 2026) introduces Exponential Residual Flows (ERF), giving discrete diffusion models a deterministic ODE sampler analogous to the probability flow ODE:
- Idea: attach a continuous residual variable to each token position; residuals evolve deterministically via piecewise-defined ODEs whose vector fields depend on the current discrete state and the model's forward/backward rate matrices. The discrete state jumps whenever a residual hits zero.
- Theory: the construction provably preserves the marginals of the original diffusion.
- Practice: a practical discretization specialized to masked and uniform diffusion; deterministic trajectories support consistency distillation for faster sampling.
- Empirically improves over prior approaches on code and text generation benchmarks.
Authors include Eric P. Xing and Alain Durmus.
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