# Diffusion Methods for Generating Transition Paths

arXiv: https://arxiv.org/abs/2309.10276 · HTML: https://mlsanity.com/paper/2309.10276/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 19 Sep 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 30)

- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [StackGAN++: Realistic Image Synthesis with Stacked Generative Adversarial Networks](https://mlsanity.com/paper/1710.10916/) (2017)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [ProDiff: Progressive Fast Diffusion Model For High-Quality Text-to-Speech](https://mlsanity.com/paper/2207.06389/) (2022)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [Solving for high dimensional committor functions using artificial neural networks](https://mlsanity.com/paper/1802.10275/) (2018)
- [User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems](https://mlsanity.com/paper/2306.07526/) (2023)
- [Computing Committor Functions for the Study of Rare Events Using Deep Learning](https://mlsanity.com/paper/1906.06285/) (2019)
- [Stochastic bridges of linear systems](https://mlsanity.com/paper/1407.3421/) (2014)
- [Generative methods for sampling transition paths in molecular dynamics](https://mlsanity.com/paper/2205.02818/) (2022)
- [Optimal control for sampling the transition path process and estimating rates](https://mlsanity.com/paper/2305.17112/) (2023)
- [Segmentation Guided Image-to-Image Translation with Adversarial Networks](https://mlsanity.com/paper/1901.01569/) (2019)

## Built on by (most cited first, 8 of 8)

- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplers](https://mlsanity.com/paper/2405.19961/) (2024)
- [Generative Model for Constructing Reaction Path from Initial to Final States](https://mlsanity.com/paper/2401.10721/) (2024)
- [New algorithms for sampling and diffusion models](https://mlsanity.com/paper/2406.09665/) (2024)
- [Analytic Bridge Diffusions for Controlled Path Generation](https://mlsanity.com/paper/2605.02961/) (2026)
- [Machine-Learned Sampling of Conditioned Path Measures](https://mlsanity.com/paper/2506.01904/) (2025)
- [Stochastic Control Policies for Robust Molecular Transition Path Sampling](https://mlsanity.com/paper/2608.13800/) (2026)
- [Machine learning kinetics from molecular dynamics data](https://mlsanity.com/paper/2609.17736/) (2026)

## Abstract (arXiv)

In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is often difficult to obtain. We develop two novel methods for path generation in this paper: a chain-based approach and a midpoint-based approach. The first biases the original dynamics to facilitate transitions, while the second mirrors splitting techniques and breaks down the original transition into smaller transitions. Numerical results of generated transition paths for the M"uller potential and for Alanine dipeptide demonstrate the effectiveness of these approaches in both the data-rich and data-scarce regimes.