# A Jump-Diffusion Framework for Irregular Time Series Generation

arXiv: https://arxiv.org/abs/2505.23215 · HTML: https://mlsanity.com/paper/2505.23215/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [KL Convergence Guarantees for Score diffusion models under minimal data assumptions](https://mlsanity.com/paper/2308.12240/) (2023)
- [From Denoising Diffusions to Denoising Markov Models](https://mlsanity.com/paper/2211.03595/) (2022)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation](https://mlsanity.com/paper/2303.04772/) (2023)
- [Trans-Dimensional Generative Modeling via Jump Diffusion Models](https://mlsanity.com/paper/2305.16261/) (2023)
- [Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering](https://mlsanity.com/paper/2006.04727/) (2020)
- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans](https://mlsanity.com/paper/2501.16839/) (2025)
- [Probabilistic Forecasting via Autoregressive Flow Matching](https://mlsanity.com/paper/2503.10375/) (2025)
- [Schr"odinger Bridge Problem for Jump Diffusions](https://mlsanity.com/paper/2411.13765/) (2024)

## Built on by (most cited first, 2 of 2)

- [Is Flow Matching Just Trajectory Replay for Sequential Data?](https://mlsanity.com/paper/2602.08318/) (2026)
- [Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics](https://mlsanity.com/paper/2604.17670/) (2026)

## Abstract (arXiv)

We propose a framework for generative modeling of continuous-time processes from irregularly and asynchronously recorded data. It is based on the matching of generators and accommodates discontinuous trajectories. Analytical formulas for diffusion and jump bridges yield a family of reference generators that a neural network is trained to match. The key ingredient is that, for our constructed jump bridge, a parametrization of the jump kernel densities by scaled Gaussians admits closed-form expressions for the Kullback-Leibler divergence, allowing simulation-free training.