Sig-DEG for Distillation: Making Diffusion Models Faster and Lighter

Abstract:Diffusion models achieve state-of-the-art generative performance but remain computationally expensive at inference, often requiring many discretization steps. We propose Sig-DEG (Signature-based Differential Equation Generator), a generator for distilling pre-trained diffusion models. Inspired by high-order stochastic Taylor expansions, Sig-DEG combines partial signatures that summarize Brownian motion over subintervals with a recurrent structure to approximate stochastic differential equation solutions to achieve universality. We formulate distillation as supervised learning, matching fine-resolution teacher trajectories on a coarse time grid. At inference, Sig-DEG enables fast generation, as the partial signatures can be simulated exactly from their known distributions without requiring fine-grained Brownian paths. Experiments on image and time-series generation demonstrate competitive sample quality with inference speedups of up to several hundred times over the teacher. A Schrödinger bridge example further demonstrates Sig-DEG's applicability beyond diffusion distillation.

44 pages. Revised version with expanded theoretical analysis, updated experiments, and revised presentation

Machine Learning (cs.LG); Probability (math.PR); Machine Learning (stat.ML)

arXiv:2508.16939 [cs.LG]

(or arXiv:2508.16939v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2508.16939 Focus to learn more arXiv-issued DOI via DataCite

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