用简化模型逼近扩散桥，提速增效还更可解释。
On Approaches to Building Surrogate ODE Models for Diffusion Bridges
- 用稀疏回归从数据中提取符号化微分方程，构建可解释的代理模型。
- 在高斯传输和MNIST潜空间任务上，性能接近原模型但推理快数个量级。
- 适合需要高效部署、可解释生成模型的工程场景。
扩散桥与薛定谔桥模型在生成建模中表现优异，但计算成本高且训练复杂。尽管连续时间桥模型能加速采样，其最优动力学常由过参数化神经网络描述，导致随机微分方程难以高效求解。本文提出一种新范式：利用代理模型对这些动力学进行简化、快速且灵活的近似。提出两种算法：基于稀疏回归的符号化微分方程识别方法（SINDy-FM），以及将薛定谔桥重构为神经ODE的形式（DSBM-NeuralODE）。在高斯传输任务和MNIST潜空间转换实验中，代理模型达到与原模型相当的性能，同时显著提升效率与可解释性。特别是符号化SINDy-FM模型，参数量减少多个数量级，实现近乎即时推理，为实际部署提供了一类可计算且高性能的桥模型。
原文摘要 · Abstract (English)
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.
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