# Score matching for bridges without learning time-reversals

arXiv: https://arxiv.org/abs/2407.15455 · HTML: https://mlsanity.com/paper/2407.15455/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 22 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [Infinite-dimensional Diffusion Bridge Simulation via Operator Learning](https://mlsanity.com/paper/2405.18353/) (2024)
- [What's the score? Automated Denoising Score Matching for Nonlinear Diffusions](https://mlsanity.com/paper/2407.07998/) (2024)
- [Automatic Backward Filtering Forward Guiding for Markov processes and graphical models](https://mlsanity.com/paper/2010.03509/) (2020)
- [A Stochastic Large Deformation Model for Computational Anatomy](https://mlsanity.com/paper/1612.05323/) (2016)

## Built on by (most cited first, 5 of 5)

- [Supervised Guidance Training for Infinite-Dimensional Diffusion Models](https://mlsanity.com/paper/2601.20756/) (2026)
- [Diffusion differentiable resampling](https://mlsanity.com/paper/2512.10401/) (2025)
- [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026)
- [Neural Backward Filtering Forward Guiding](https://mlsanity.com/paper/2601.23030/) (2026)
- [Reflected Schr"odinger Bridge Matching](https://mlsanity.com/paper/2607.03626/) (2026)

## Abstract (arXiv)

We propose a new algorithm for learning bridged diffusion processes using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob's h-transform, yields a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, we learn the score term nablax log p(t, x; T, y) directly, for given t, y, completely avoiding first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at https://github.com/libbylbaker/forwardbridge.