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Main Authors: Khilchuk, Maria, Latypov, Vladimir, Kleshchev, Pavel, Hvatov, Alexander
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.12671
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author Khilchuk, Maria
Latypov, Vladimir
Kleshchev, Pavel
Hvatov, Alexander
author_facet Khilchuk, Maria
Latypov, Vladimir
Kleshchev, Pavel
Hvatov, Alexander
contents Diffusion and Schrödinger Bridge models have established state-of-the-art performance in generative modeling but are often hampered by significant computational costs and complex training procedures. While continuous-time bridges promise faster sampling, overparameterized neural networks describe their optimal dynamics, and the underlying stochastic differential equations can be difficult to integrate efficiently. This work introduces a novel paradigm that uses surrogate models to create simpler, faster, and more flexible approximations of these dynamics. We propose two specific algorithms: SINDy Flow Matching (SINDy-FM), which leverages sparse regression to identify interpretable, symbolic differential equations from data, and a Neural-ODE reformulation of the Schrödinger Bridge (DSBM-NeuralODE) for flexible continuous-time parameterization. Our experiments on Gaussian transport tasks and MNIST latent translation demonstrate that these surrogates achieve competitive performance while offering dramatic improvements in efficiency and interpretability. The symbolic SINDy-FM models, in particular, reduce parameter counts by several orders of magnitude and enable near-instantaneous inference, paving the way for a new class of tractable and high-performing bridge models for practical deployment.
format Preprint
id arxiv_https___arxiv_org_abs_2512_12671
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Approaches to Building Surrogate ODE Models for Diffusion Bridges
Khilchuk, Maria
Latypov, Vladimir
Kleshchev, Pavel
Hvatov, Alexander
Machine Learning
Diffusion and Schrödinger Bridge models have established state-of-the-art performance in generative modeling but are often hampered by significant computational costs and complex training procedures. While continuous-time bridges promise faster sampling, overparameterized neural networks describe their optimal dynamics, and the underlying stochastic differential equations can be difficult to integrate efficiently. This work introduces a novel paradigm that uses surrogate models to create simpler, faster, and more flexible approximations of these dynamics. We propose two specific algorithms: SINDy Flow Matching (SINDy-FM), which leverages sparse regression to identify interpretable, symbolic differential equations from data, and a Neural-ODE reformulation of the Schrödinger Bridge (DSBM-NeuralODE) for flexible continuous-time parameterization. Our experiments on Gaussian transport tasks and MNIST latent translation demonstrate that these surrogates achieve competitive performance while offering dramatic improvements in efficiency and interpretability. The symbolic SINDy-FM models, in particular, reduce parameter counts by several orders of magnitude and enable near-instantaneous inference, paving the way for a new class of tractable and high-performing bridge models for practical deployment.
title On Approaches to Building Surrogate ODE Models for Diffusion Bridges
topic Machine Learning
url https://arxiv.org/abs/2512.12671