# Causal Time Series Generation via Diffusion Models

arXiv: https://arxiv.org/abs/2509.20846 · HTML: https://mlsanity.com/paper/2509.20846/

## 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 33 of its 48 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## 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 33)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Learning Causal Semantic Representation for Out-of-Distribution Prediction](https://mlsanity.com/paper/2011.01681/) (2020)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [A Causal Lens for Controllable Text Generation](https://mlsanity.com/paper/2201.09119/) (2022)
- [Conditional GAN for timeseries generation](https://mlsanity.com/paper/2006.16477/) (2020)
- [Time Weaver: A Conditional Time Series Generation Model](https://mlsanity.com/paper/2403.02682/) (2024)
- [T-CGAN: Conditional Generative Adversarial Network for Data Augmentation in Noisy Time Series with Irregular Sampling](https://mlsanity.com/paper/1811.08295/) (2018)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [TimeDP: Learning to Generate Multi-Domain Time Series with Domain Prompts](https://mlsanity.com/paper/2501.05403/) (2025)
- [BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modeling](https://mlsanity.com/paper/2503.02445/) (2025)

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

- [Interventional Time Series Priors for Causal Foundation Models](https://mlsanity.com/paper/2603.11090/) (2026)
- [Towards Continuous-time Causal Foundation Models](https://mlsanity.com/paper/2605.28880/) (2026)
- [OATS: Online Data Augmentation for Time Series Foundation Models](https://mlsanity.com/paper/2601.19040/) (2026)
- [Diff-MN: Diffusion Parameterized MoE-NCDE for Continuous Time Series Generation with Irregular Observations](https://mlsanity.com/paper/2601.13534/) (2026)
- [Causal Diffusion Models for Counterfactual Outcome Distributions in Longitudinal Data](https://mlsanity.com/paper/2604.12992/) (2026)
- [Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions](https://mlsanity.com/paper/2605.09870/) (2026)
- [Learning Spatio-Temporal Foundation Models from Pure Synthetic Data](https://mlsanity.com/paper/2607.16251/) (2026)
- [Amortized Interventional Forecasting for Multivariate CIR Processes](https://mlsanity.com/paper/2608.03715/) (2026)

## Abstract (arXiv)

Time series generation (TSG) synthesizes realistic sequences and has achieved remarkable success. Among TSG, conditional models generate sequences given observed covariates, however, such models learn observational correlations without considering unobserved confounding. In this work, we propose a causal perspective on conditional TSG and introduce causal time series generation as a new TSG task family, formalized within Pearl's causal ladder, extending beyond observational generation to include interventional and counterfactual settings. To instantiate these tasks, we develop CaTSG, a unified diffusion-based framework with backdoor-adjusted guidance that causally steers sampling toward desired interventions and individual counterfactuals while preserving observational fidelity. Specifically, our method derives causal score functions via backdoor adjustment and the abduction-action-prediction procedure, thus enabling principled support for all three levels of TSG. Extensive experiments on both synthetic and real-world datasets show that CaTSG achieves superior fidelity and also supporting interventional and counterfactual generation that existing baselines cannot handle. Overall, we propose the causal TSG family and instantiate it with CaTSG, providing an initial proof-of-concept and opening a promising direction toward more reliable simulation under interventions and counterfactual generation.