# Conditional Loss and Deep Euler Scheme for Time Series Generation

arXiv: https://arxiv.org/abs/2102.05313 · HTML: https://mlsanity.com/paper/2102.05313/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 10 Feb 2021.

## Builds on (most cited first, 23 of 23)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [MoCoGAN: Decomposing Motion and Content for Video Generation](https://mlsanity.com/paper/1707.04993/) (2017)
- [Generating Videos with Scene Dynamics](https://mlsanity.com/paper/1609.02612/) (2016)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Temporal Generative Adversarial Nets with Singular Value Clipping](https://mlsanity.com/paper/1611.06624/) (2016)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Adversarial Feature Matching for Text Generation](https://mlsanity.com/paper/1706.03850/) (2017)
- [Model-Free Renewable Scenario Generation Using Generative Adversarial Networks](https://mlsanity.com/paper/1707.09676/) (2017)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [Adversarial Video Generation on Complex Datasets](https://mlsanity.com/paper/1907.06571/) (2019)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [Improving Clinical Predictions through Unsupervised Time Series Representation Learning](https://mlsanity.com/paper/1812.00490/) (2018)
- [Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions](https://mlsanity.com/paper/1805.07594/) (2018)

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

- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [PCF-GAN: generating sequential data via the characteristic function of measures on the path space](https://mlsanity.com/paper/2305.12511/) (2023)
- [New Money: A Systematic Review of Synthetic Data Generation for Finance](https://mlsanity.com/paper/2510.26076/) (2025)
- [CTBench: Cryptocurrency Time Series Generation Benchmark](https://mlsanity.com/paper/2508.02758/) (2025)

## Abstract (arXiv)

We introduce three new generative models for time series that are based on Euler discretization of Stochastic Differential Equations (SDEs) and Wasserstein metrics. Two of these methods rely on the adaptation of generative adversarial networks (GANs) to time series. The third algorithm, called Conditional Euler Generator (CEGEN), minimizes a dedicated distance between the transition probability distributions over all time steps. In the context of Ito processes, we provide theoretical guarantees that minimizing this criterion implies accurate estimations of the drift and volatility parameters. We demonstrate empirically that CEGEN outperforms state-of-the-art and GAN generators on both marginal and temporal dynamics metrics. Besides, it identifies accurate correlation structures in high dimension. When few data points are available, we verify the effectiveness of CEGEN, when combined with transfer learning methods on Monte Carlo simulations. Finally, we illustrate the robustness of our method on various real-world datasets.