# Generative modelling with jump-diffusions

arXiv: https://arxiv.org/abs/2503.06558 · HTML: https://mlsanity.com/paper/2503.06558/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 20 of 20)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [From Denoising Diffusions to Denoising Markov Models](https://mlsanity.com/paper/2211.03595/) (2022)
- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [Trans-Dimensional Generative Modeling via Jump Diffusion Models](https://mlsanity.com/paper/2305.16261/) (2023)
- [Denoising Diffusion Gamma Models](https://mlsanity.com/paper/2110.05948/) (2021)
- [Heavy-tailed denoising score matching](https://mlsanity.com/paper/2112.09788/) (2021)
- [Heavy-Tailed Diffusion with Denoising L'evy Probabilistic Models](https://mlsanity.com/paper/2407.18609/) (2024)
- [Generative Fractional Diffusion Models](https://mlsanity.com/paper/2310.17638/) (2023)
- [Non-Normal Diffusion Models](https://mlsanity.com/paper/2412.07935/) (2024)

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

- [Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models](https://mlsanity.com/paper/2506.03849/) (2025)
- [Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training](https://mlsanity.com/paper/2605.13175/) (2026)
- [An effective potential for generative modelling with active matter](https://mlsanity.com/paper/2508.08146/) (2025)
- [Heavy-Tailed Flow Matching via Random Clocks](https://mlsanity.com/paper/2607.13841/) (2026)
- [Radial Tail Repair: Post-Training Correction for Diffusion and Flow Models](https://mlsanity.com/paper/2610.16851/) (2026)

## Abstract (arXiv)

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.