# On Approaches to Building Surrogate ODE Models for Diffusion Bridges

arXiv: https://arxiv.org/abs/2512.12671 · HTML: https://mlsanity.com/paper/2512.12671/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 30 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [HunyuanImage 3.0 Technical Report](https://mlsanity.com/paper/2509.23951/) (2025)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [The Schr"odinger Bridge between Gaussian Measures has a Closed Form](https://mlsanity.com/paper/2202.05722/) (2022)
- [Deep Generalized Schr"odinger Bridge](https://mlsanity.com/paper/2209.09893/) (2022)
- [Schr"odinger Bridge Flow for Unpaired Data Translation](https://mlsanity.com/paper/2409.09347/) (2024)
- [A Survey on Cache Methods in Diffusion Models: Toward Efficient Multi-Modal Generation](https://mlsanity.com/paper/2510.19755/) (2025)
- [DyPE: Dynamic Position Extrapolation for Ultra High Resolution Diffusion](https://mlsanity.com/paper/2510.20766/) (2025)
- [Adversarial Schr"odinger Bridge Matching](https://mlsanity.com/paper/2405.14449/) (2024)
- [GeoGen: A Two-stage Coarse-to-Fine Framework for Fine-grained Synthetic Location-based Social Network Trajectory Generation](https://mlsanity.com/paper/2510.07735/) (2025)
- [Stable Diffusion Dataset Generation for Downstream Classification Tasks](https://mlsanity.com/paper/2405.02698/) (2024)
- [Diffusion & Adversarial Schr"odinger Bridges via Iterative Proportional Markovian Fitting](https://mlsanity.com/paper/2410.02601/) (2024)
- [The Rise of Generative AI for Metal-Organic Framework Design and Synthesis](https://mlsanity.com/paper/2508.13197/) (2025)
- [Guided Diffusion for the Discovery of New Superconductors](https://mlsanity.com/paper/2509.25186/) (2025)
- [Step-Aware Residual-Guided Diffusion for EEG Spatial Super-Resolution](https://mlsanity.com/paper/2510.19166/) (2025)
- [Flow marching for a generative PDE foundation model](https://mlsanity.com/paper/2509.18611/) (2025)
- [MolSnap: Snap-Fast Molecular Generation with Latent Variational Mean Flow](https://mlsanity.com/paper/2508.05411/) (2025)

## Abstract (arXiv)

Diffusion and Schr"odinger 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 Schr"odinger 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.