# Piecewise deterministic generative models

arXiv: https://arxiv.org/abs/2407.19448 · HTML: https://mlsanity.com/paper/2407.19448/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 28 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Diff-TTS: A Denoising Diffusion Model for Text-to-Speech](https://mlsanity.com/paper/2104.01409/) (2021)
- [The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method](https://mlsanity.com/paper/1510.02451/) (2015)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [Stereographic Markov Chain Monte Carlo](https://mlsanity.com/paper/2205.12112/) (2022)
- [Piecewise Deterministic Markov Processes for Scalable Monte Carlo on Restricted Domains](https://mlsanity.com/paper/1701.04244/) (2017)
- [Approximations of Piecewise Deterministic Markov Processes and their convergence properties](https://mlsanity.com/paper/2109.11827/) (2021)

## Built on by (most cited first, 4 of 4)

- [Non-Asymptotic Convergence of Discrete Diffusion Models: Masked and Random Walk dynamics](https://mlsanity.com/paper/2512.00580/) (2025)
- [Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models](https://mlsanity.com/paper/2506.03849/) (2025)
- [Bouncy particle sampler with infinite exchanging parallel tempering](https://mlsanity.com/paper/2509.02003/) (2025)
- [Beyond Two-stage Diffusion TTS: Joint Structure and Content Refinement via Jump Diffusion](https://mlsanity.com/paper/2603.14032/) (2026)

## Abstract (arXiv)

We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to diffusions, such Markov processes admit time reversals that turn out to be PDMPs as well. We apply this observation to three PDMPs considered in the literature: the Zig-Zag process, Bouncy Particle Sampler, and Randomised Hamiltonian Monte Carlo. For these three particular instances, we show that the jump rates and kernels of the corresponding time reversals admit explicit expressions depending on some conditional densities of the PDMP under consideration before and after a jump. Based on these results, we propose efficient training procedures to learn these characteristics and consider methods to approximately simulate the reverse process. Finally, we provide bounds in the total variation distance between the data distribution and the resulting distribution of our model in the case where the base distribution is the standard d-dimensional Gaussian distribution. Promising numerical simulations support further investigations into this class of models.