Data to 7 Oct 2026

COT-GAN: Generating Sequential Data via Causal Optimal Transport

arXiv 2006.08571 ↗First posted 15 Jun 2020stat.ML cs.LGcited by 70

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Abstract (arXiv)

We introduce COT-GAN, an adversarial algorithm to train implicit generative models optimized for producing sequential data. The loss function of this algorithm is formulated using ideas from Causal Optimal Transport (COT), which combines classic optimal transport methods with an additional temporal causality constraint. Remarkably, we find that this causality condition provides a natural framework to parameterize the cost function that is learned by the discriminator as a robust (worst-case) distance, and an ideal mechanism for learning time dependent data distributions. Following Genevay et al. (2018), we also include an entropic penalization term which allows for the use of the Sinkhorn algorithm when computing the optimal transport cost. Our experiments show effectiveness and stability of COT-GAN when generating both low- and high-dimensional time series data. The success of the algorithm also relies on a new, improved version of the Sinkhorn divergence which demonstrates less bias in learning.

Key facts. Cited by 70 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Jun 2020.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 16; 2024: 12; 2025: 20; 2026: 8.

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2023Diffusion Models for Time Series Applications: A Surveycited by 72
2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 48
2021Towards Generating Real-World Time Series Datacited by 26
2023TSGBench: Time Series Generation Benchmarkcited by 24
2022Generating multivariate time series with COmmon Source CoordInated GAN (COSCI-GAN)cited by 23
2023Regular Time-series Generation using SGMcited by 23
2024FlowTS: Time Series Generation via Rectified Flowcited by 22
2023Generative modeling for time series via Schr"odinger bridgecited by 18
2021SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Losscited by 13
2023PCF-GAN: generating sequential data via the characteristic function of measures on the path spacecited by 13
2023TransFusion: Generating Long, High Fidelity Time Series using Diffusion Models with Transformerscited by 13
2021A Multi-scale Time-series Dataset with Benchmark for Machine Learning in Decarbonized Energy Gridscited by 11

38 more

2022Time-series Transformer Generative Adversarial Networkscited by 10
2023Emerging Synergies in Causality and Deep Generative Models: A Surveycited by 10
2024TimeLDM: Latent Diffusion Model for Unconditional Time Series Generationcited by 10
2022Existence and Estimation of Critical Batch Size for Training Generative Adversarial Networks with Two Time-Scale Update Rulecited by 8
2023Time-series Generation by Contrastive Imitationcited by 8
2024Time-Causal VAE: Robust Financial Time Series Generatorcited by 8
2023The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNscited by 7
2025Robust time series generation via Schr"odinger Bridge: a comprehensive evaluationcited by 7
2021Generative modeling of spatio-temporal weather patterns with extreme event conditioningcited by 6
2024Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficientlycited by 6
2024TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generationcited by 5
2024Neural Spacetimes for DAG Representation Learningcited by 5
2021Conditional Loss and Deep Euler Scheme for Time Series Generationcited by 4
2024Universal randomised signatures for generative time series modellingcited by 4
2025WaveStitch: Flexible and Fast Conditional Time Series Generation with Diffusion Modelscited by 4
2021Conditional COT-GAN for Video Prediction with Kernel Smoothingcited by 3
2024High Rank Path Development: an approach of learning the filtration of stochastic processescited by 3
2025MSDformer: Multi-scale Discrete Transformer For Time Series Generationcited by 3
2025CTBench: Cryptocurrency Time Series Generation Benchmarkcited by 3
2025T2I-Diff: fMRI Signal Generation via Time-Frequency Image Transform and Classifier-Free Denoising Diffusion Modelscited by 3
2025TSGM: Regular and Irregular Time-series Generation using Score-based Generative Modelscited by 3
2026SDFlow: Similarity-Driven Flow Matching for Time Series Generationcited by 3
2021Generative Adversarial Network: Some Analytical Perspectivescited by 2
2023Information-Theoretic GAN Compression with Variational Energy-based Modelcited by 2
2023Fitted value iteration methods for bicausal optimal transportcited by 2
2025Distances for Markov chains from sample streamscited by 2
2025Distributional Adversarial Attacks and Training in Deep Hedgingcited by 2
2025Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysiscited by 2
2025Sequence Modeling with Spectral Mean Flowscited by 2
2025TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modelingcited by 2
2025Towards Stable and Structured Time Series Generation with Perturbation-Aware Flow Matchingcited by 2
2026Functional MRI Time Series Generation via Wavelet-Based Image Transform and Spectral Flow Matching for Brain Disorder Identificationcited by 2
2022Distributionally robust risk evaluation with a causality constraint and structural informationcited by 1
2023Fully Embedded Time-Series Generative Adversarial Networkscited by 1
2024MCGAN: Enhancing GAN Training with Regression-Based Generator Losscited by 1
2024Auditing and Enforcing Conditional Fairness via Optimal Transportcited by 1
2024Domain Fusion Controllable Generalization for Cross-Domain Time Series Forecasting from Multi-Domain Integrated Distributioncited by 1
2025FaultDiffusion: Few-Shot Fault Time Series Generation with Diffusion Modelcited by 1

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