# Private Continuous-Time Synthetic Trajectory Generation via Mean-Field Langevin Dynamics

arXiv: https://arxiv.org/abs/2506.12203 · HTML: https://mlsanity.com/paper/2506.12203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 59 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 29 of 29)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Differentially Private Diffusion Models](https://mlsanity.com/paper/2210.09929/) (2022)
- [DP-CGAN: Differentially Private Synthetic Data and Label Generation](https://mlsanity.com/paper/2001.09700/) (2020)
- [Deep Learning with Gaussian Differential Privacy](https://mlsanity.com/paper/1911.11607/) (2019)
- [Convex Analysis of the Mean Field Langevin Dynamics](https://mlsanity.com/paper/2201.10469/) (2022)
- [Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport](https://mlsanity.com/paper/2410.00844/) (2024)
- [Trajectory Inference via Mean-field Langevin in Path Space](https://mlsanity.com/paper/2205.07146/) (2022)
- [Multi-marginal Schr"odinger Bridges with Iterative Reference Refinement](https://mlsanity.com/paper/2408.06277/) (2024)
- [LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scale](https://mlsanity.com/paper/2002.05839/) (2020)
- [Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction](https://mlsanity.com/paper/2306.07221/) (2023)
- [Differentially Private Release of Israel's National Registry of Live Births](https://mlsanity.com/paper/2405.00267/) (2024)
- [LDPTrace: Locally Differentially Private Trajectory Synthesis](https://mlsanity.com/paper/2302.06180/) (2023)
- [PrivTrace: Differentially Private Trajectory Synthesis by Adaptive Markov Model](https://mlsanity.com/paper/2210.00581/) (2022)
- [Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Prior](https://mlsanity.com/paper/2406.07475/) (2024)
- [Improved Particle Approximation Error for Mean Field Neural Networks](https://mlsanity.com/paper/2405.15767/) (2024)
- [Algorithmically Effective Differentially Private Synthetic Data](https://mlsanity.com/paper/2302.05552/) (2023)
- [Privacy-preserving data release leveraging optimal transport and particle gradient descent](https://mlsanity.com/paper/2401.17823/) (2024)
- [Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets](https://mlsanity.com/paper/2305.17148/) (2023)
- [Online Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2402.08012/) (2024)
- [Private Geometric Median](https://mlsanity.com/paper/2406.07407/) (2024)
- [Mirror Mean-Field Langevin Dynamics](https://mlsanity.com/paper/2505.02621/) (2025)
- [Privacy without Noisy Gradients: Slicing Mechanism for Generative Model Training](https://mlsanity.com/paper/2410.19941/) (2024)

## Abstract (arXiv)

We provide an algorithm to privately generate continuous-time data (e.g. marginals from stochastic differential equations), which has applications in highly sensitive domains involving time-series data such as healthcare. We leverage the connections between trajectory inference and continuous-time synthetic data generation, along with a computational method based on mean-field Langevin dynamics. As discretized mean-field Langevin dynamics and noisy particle gradient descent are equivalent, DP results for noisy SGD can be applied to our setting. We provide experiments that generate realistic trajectories on a synthesized variation of hand-drawn MNIST data while maintaining meaningful privacy guarantees. Crucially, our method has strong utility guarantees under the setting where each person contributes data for only one time point, while prior methods require each person to contribute their entire temporal trajectory--directly improving the privacy characteristics by construction.