Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: FAIR: Framework for responsible adoption of Artificial Intelligence in the financial seRvices industry, DTP 2224 University College London, High order mathematical and computational infrastructure for streamed data that enhance contemporary generative and large language models, G2677699893, G3481878861, G3824261352, G444630160, The Alan Turing Institute, UDLA 2527 University College London, G8463344687, G8581904048, Unparameterised multi-modal data, high order signatures, and the mathematics of data science, DTP 2020-2021 University College London
OpenAlex ID: W7077880671
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