# DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series

arXiv: https://arxiv.org/abs/2511.02137 · HTML: https://mlsanity.com/paper/2511.02137/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 84 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks](https://mlsanity.com/paper/1701.05923/) (2017)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Variable Rate Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06085/) (2015)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [Causal Autoregressive Flows](https://mlsanity.com/paper/2011.02268/) (2020)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Causal normalizing flows: from theory to practice](https://mlsanity.com/paper/2306.05415/) (2023)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)

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

- [CoreFlow: Low-Rank Matrix Generative Models](https://mlsanity.com/paper/2604.24959/) (2026)
- [Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions](https://mlsanity.com/paper/2605.09870/) (2026)
- [Interventional Flow Matching: Prospective Dose-Response Forecasting with Velocity-Field Jacobian Regularization](https://mlsanity.com/paper/2606.29386/) (2026)
- [GazeDiT: Gaze-Accurate Diffusion Image Generation for Eye Tracking via Spatial Conditioning](https://mlsanity.com/paper/2609.17814/) (2026)

## Abstract (arXiv)

Time-series forecasting increasingly demands not only accurate observational predictions but also causal forecasting under interventional and counterfactual queries in multivariate systems. We present DoFlow, a flow-based generative model defined over a causal Directed Acyclic Graph (DAG) that delivers coherent observational and interventional predictions, as well as counterfactuals through the natural encoding-decoding mechanism of continuous normalizing flows (CNFs). We also provide a supporting counterfactual recovery theory under certain assumptions. Beyond forecasting, DoFlow provides explicit likelihoods of future trajectories, enabling principled anomaly detection. Experiments on synthetic datasets with various causal DAG structures and real-world hydropower and cancer-treatment time series show that DoFlow achieves accurate system-wide observational forecasting, enables causal forecasting over interventional and counterfactual queries, and effectively detects anomalies. This work contributes to the broader goal of unifying causal reasoning and generative modeling for complex dynamical systems.