2025/12/14 by Maria Khilchuk, Viktor Latypov, Khilchuk, Maria +5
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2512.12671
openalex publication_date 2025/12/14 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
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.