Evaluating approaches to surrogate ODE-based modelling of diffusion bridges

Khilchuk Maria Denisovna, Vladimir Latypov, Kleshchev Pavel Sergeevich, Alexander Hvatov

Keywords: Schrödinger Bridge, surrogate modeling, SINDy, NeuralODE

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, over parameterized 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.

Submission Number: 52