{"ID":2829307,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12671","arxiv_id":"2512.12671","title":"On Approaches to Building Surrogate ODE Models for Diffusion Bridges","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.12671","url_pdf":"https://arxiv.org/pdf/2512.12671v1","authors":"[\"Maria Khilchuk\",\"Vladimir Latypov\",\"Pavel Kleshchev\",\"Alexander Hvatov\"]","published":"2025-12-14T12:49:38Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}