On Approaches to Building Surrogate ODE Models for Diffusion Bridges

• URL: http://arxiv.org/abs/2512.12671v1
• Date: Sun, 14 Dec 2025 12:49:38 GMT
• Title: On Approaches to Building Surrogate ODE Models for Diffusion Bridges
• Authors: Maria Khilchuk, Vladimir Latypov, Pavel Kleshchev, Alexander Hvatov,
• Abstract summary: Diffusion and Schrdinger Bridge models have established state-of-the-art performance in generative modeling.<n>These models are often hampered by significant computational costs and complex training procedures.<n>This work introduces a novel paradigm that uses surrogate models to create simpler, faster, and more flexible approximations of these dynamics.
• Score: 39.92969675794945
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models [6.403678133359229]
  latent dynamics in high-dimensional recordings are often characterized by a much smaller set of effective variables.<n>Most machine learning approaches tackle these tasks jointly by training autoencoders together with models that enforce dynamical consistency.<n>We propose to decouple the two problems by leveraging the recently introduced Foundation Inference Models (FIMs)<n>A proof of concept on a double-well system with semicircle diffusion, embedded into synthetic video data, illustrates the potential of this approach for fast and reusable coarse-graining pipelines.
  arXiv  Detail & Related papers  (2025-10-14T15:17:23Z)
• Merging Models on the Fly Without Retraining: A Sequential Approach to Scalable Continual Model Merging [75.93960998357812]
  Deep model merging represents an emerging research direction that combines multiple fine-tuned models to harness their capabilities across different tasks and domains.<n>Current model merging techniques focus on merging all available models simultaneously, with weight matrices-based methods being the predominant approaches.<n>We propose a training-free projection-based continual merging method that processes models sequentially.
  arXiv  Detail & Related papers  (2025-01-16T13:17:24Z)
• Energy-Based Diffusion Language Models for Text Generation [126.23425882687195]
  Energy-based Diffusion Language Model (EDLM) is an energy-based model operating at the full sequence level for each diffusion step.<n>Our framework offers a 1.3$times$ sampling speedup over existing diffusion models.
  arXiv  Detail & Related papers  (2024-10-28T17:25:56Z)
• Switched Flow Matching: Eliminating Singularities via Switching ODEs [12.273757042838675]
  Continuous-time generative models, such as Flow Matching (FM), construct probability paths to transport between one distribution and another. During inference, however, the learned model often requires multiple neural network evaluations to accurately integrate the flow. We propose Switched FM (SFM), that eliminates singularities via switching ODEs, as opposed to using a uniform ODE in FM.
  arXiv  Detail & Related papers  (2024-05-19T16:21:04Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• The Missing U for Efficient Diffusion Models [3.712196074875643]
  Diffusion Probabilistic Models yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse process, remains a challenge due to slow convergence rates and high computational costs. We introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models.
  arXiv  Detail & Related papers  (2023-10-31T00:12:14Z)
• Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems [0.0]
  In absence of governing equations, we need to construct the parametric reduced-order surrogate model in a non-intrusive fashion. Our work provides a non-intrusive optimality criterion to efficiently populate the parameter snapshots. We propose an active-learning-driven surrogate model using kernel-based shallow neural networks.
  arXiv  Detail & Related papers  (2023-06-09T18:01:14Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems [14.553972457854517]
  We present a data-driven, space-time continuous framework to learn surrogatemodels for complex physical systems. We leverage the expressive power of the network and aspecially designed consistency-inducing regularization to obtain latent trajectories that are both low-dimensional and smooth.
  arXiv  Detail & Related papers  (2023-01-25T03:06:03Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.