# Causal Recurrent Variational Autoencoder for Medical Time Series Generation

arXiv: https://arxiv.org/abs/2301.06574 · HTML: https://mlsanity.com/paper/2301.06574/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 16 Jan 2023.

## Builds on (most cited first, 14 of 14)

- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Variational Recurrent Auto-Encoders](https://mlsanity.com/paper/1412.6581/) (2014)
- [Z-Forcing: Training Stochastic Recurrent Networks](https://mlsanity.com/paper/1711.05411/) (2017)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Direct coupling information measure from non-uniform embedding](https://mlsanity.com/paper/1305.6204/) (2013)

## Built on by (most cited first, 30 of 45)

- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [Generative AI for Synthetic Data Across Multiple Medical Modalities: A Systematic Review of Recent Developments and Challenges](https://mlsanity.com/paper/2407.00116/) (2024)
- [TimeDP: Learning to Generate Multi-Domain Time Series with Domain Prompts](https://mlsanity.com/paper/2501.05403/) (2025)
- [Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting](https://mlsanity.com/paper/2305.09703/) (2023)
- [Time Series Generation Under Data Scarcity: A Unified Generative Modeling Approach](https://mlsanity.com/paper/2505.20446/) (2025)
- [Time Evidence Fusion Network: Multi-source View in Long-Term Time Series Forecasting](https://mlsanity.com/paper/2405.06419/) (2024)
- [Jacobian Regularizer-based Neural Granger Causality](https://mlsanity.com/paper/2405.08779/) (2024)
- [Towards Identifiability of Hierarchical Temporal Causal Representation Learning](https://mlsanity.com/paper/2510.18310/) (2025)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [Learning Reconfigurable Representations for Multimodal Federated Learning with Missing Data](https://mlsanity.com/paper/2510.22880/) (2025)
- [Embracing the black box: Heading towards foundation models for causal discovery from time series data](https://mlsanity.com/paper/2402.09305/) (2024)
- [Time-Transformer: Integrating Local and Global Features for Better Time Series Generation (Extended Version)](https://mlsanity.com/paper/2312.11714/) (2023)
- [Peri-midFormer: Periodic Pyramid Transformer for Time Series Analysis](https://mlsanity.com/paper/2411.04554/) (2024)
- [Towards Controllable Time Series Generation](https://mlsanity.com/paper/2403.03698/) (2024)
- [Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Data](https://mlsanity.com/paper/2406.10419/) (2024)
- [CTBench: Cryptocurrency Time Series Generation Benchmark](https://mlsanity.com/paper/2508.02758/) (2025)
- [HaHeAE: Learning Generalisable Joint Representations of Human Hand and Head Movements in Extended Reality](https://mlsanity.com/paper/2410.16430/) (2024)
- [UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems](https://mlsanity.com/paper/2511.03168/) (2025)
- [TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling](https://mlsanity.com/paper/2511.07968/) (2025)
- [Fully Embedded Time-Series Generative Adversarial Networks](https://mlsanity.com/paper/2308.15730/) (2023)
- [T-CACE: A Time-Conditioned Autoregressive Contrast Enhancement Multi-Task Framework for Contrast-Free Liver MRI Synthesis, Segmentation, and Diagnosis](https://mlsanity.com/paper/2508.09919/) (2025)
- [Stage-Diff: Stage-wise Long-Term Time Series Generation Based on Diffusion Models](https://mlsanity.com/paper/2508.21330/) (2025)
- [DLGAN : Time Series Synthesis Based on Dual-Layer Generative Adversarial Networks](https://mlsanity.com/paper/2508.21340/) (2025)
- [TransConv-DDPM: Enhanced Diffusion Model for Generating Time-Series Data in Healthcare](https://mlsanity.com/paper/2602.07033/) (2026)
- [MLE-UVAD: Minimal Latent Entropy Autoencoder for Fully Unsupervised Video Anomaly Detection](https://mlsanity.com/paper/2603.23868/) (2026)
- [PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders](https://mlsanity.com/paper/2609.05212/) (2026)
- [Exploring Diffusion Transformers for Cross-Modal Augmentation in Multimodal Brain State Decoding](https://mlsanity.com/paper/2609.11341/) (2026)

## Abstract (arXiv)

We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the p-th head is responsible for generating the p-th dimension of x (i.e., xp). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adjacency matrix that encodes causal relations between all pairs of variables. Thanks to this causal matrix, our decoder strictly obeys the underlying principles of Granger causality, thereby making the data generating process transparent. We develop a two-stage approach to train the overall objective. Empirically, we evaluate the behavior of our model in synthetic data and two real-world human brain datasets involving, respectively, the electroencephalography (EEG) signals and the functional magnetic resonance imaging (fMRI) data. Our model consistently outperforms state-of-the-art time series generative models both qualitatively and quantitatively. Moreover, it also discovers a faithful causal graph with similar or improved accuracy over existing Granger causality-based causal inference methods. Code of CR-VAE is publicly available at https://github.com/hongmingli1995/CR-VAE.