# On the Constrained Time-Series Generation Problem

arXiv: https://arxiv.org/abs/2307.01717 · HTML: https://mlsanity.com/paper/2307.01717/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 65 references that are in the map.
- First posted on arXiv 4 Jul 2023.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [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)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [Objective-Reinforced Generative Adversarial Networks (ORGAN) for Sequence Generation Models](https://mlsanity.com/paper/1705.10843/) (2017)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networks](https://mlsanity.com/paper/2210.02040/) (2022)
- [Get Real: Realism Metrics for Robust Limit Order Book Market Simulations](https://mlsanity.com/paper/1912.04941/) (2019)
- [Deep Latent State Space Models for Time-Series Generation](https://mlsanity.com/paper/2212.12749/) (2022)

## Built on by (most cited first, 30 of 54)

- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modeling](https://mlsanity.com/paper/2503.02445/) (2025)
- [Population Aware Diffusion for Time Series Generation](https://mlsanity.com/paper/2501.00910/) (2025)
- [Time Series Generation Under Data Scarcity: A Unified Generative Modeling Approach](https://mlsanity.com/paper/2505.20446/) (2025)
- [TimeLDM: Latent Diffusion Model for Unconditional Time Series Generation](https://mlsanity.com/paper/2407.04211/) (2024)
- [One-Step Offline Distillation of Diffusion-based Models via Koopman Modeling](https://mlsanity.com/paper/2505.13358/) (2025)
- [Multi-Modal Financial Time-Series Retrieval Through Latent Space Projections](https://mlsanity.com/paper/2309.16741/) (2023)
- [Causal Time Series Generation via Diffusion Models](https://mlsanity.com/paper/2509.20846/) (2025)
- [Constrained Posterior Sampling: Time Series Generation with Hard Constraints](https://mlsanity.com/paper/2410.12652/) (2024)
- [Modeling Human Gaze Behavior with Diffusion Models for Unified Scanpath Prediction](https://mlsanity.com/paper/2507.23021/) (2025)
- [A Diffusion Model for Regular Time Series Generation from Irregular Data with Completion and Masking](https://mlsanity.com/paper/2510.06699/) (2025)
- [TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generation](https://mlsanity.com/paper/2408.06672/) (2024)
- [A Financial Time Series Denoiser Based on Diffusion Model](https://mlsanity.com/paper/2409.02138/) (2024)
- [SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2401.08119/) (2024)
- [A Survey of Transformer Enabled Time Series Synthesis](https://mlsanity.com/paper/2406.02322/) (2024)
- [Loss Shaping Constraints for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2402.09373/) (2024)
- [IT-OSE: Exploring Optimal Sample Size for Industrial Data Augmentation](https://mlsanity.com/paper/2602.15878/) (2026)
- [BioMamba: Leveraging Spectro-Temporal Embedding in Bidirectional Mamba for Enhanced Biosignal Classification](https://mlsanity.com/paper/2503.11741/) (2025)
- [MSDformer: Multi-scale Discrete Transformer For Time Series Generation](https://mlsanity.com/paper/2505.14202/) (2025)
- [CTBench: Cryptocurrency Time Series Generation Benchmark](https://mlsanity.com/paper/2508.02758/) (2025)
- [T2I-Diff: fMRI Signal Generation via Time-Frequency Image Transform and Classifier-Free Denoising Diffusion Models](https://mlsanity.com/paper/2509.20822/) (2025)
- [SDFlow: Similarity-Driven Flow Matching for Time Series Generation](https://mlsanity.com/paper/2605.05736/) (2026)
- [Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.02168/) (2024)
- [Forecasting time series with constraints](https://mlsanity.com/paper/2502.10485/) (2025)
- [DS-Diffusion: Data Style-Guided Diffusion Model for Time-Series Generation](https://mlsanity.com/paper/2509.18584/) (2025)
- [Sequence Modeling with Spectral Mean Flows](https://mlsanity.com/paper/2510.15366/) (2025)
- [TimeFlow: Towards Stochastic-Aware and Efficient Time Series Generation via Flow Matching Modeling](https://mlsanity.com/paper/2511.07968/) (2025)

## Abstract (arXiv)

Synthetic time series are often used in practical applications to augment the historical time series dataset for better performance of machine learning algorithms, amplify the occurrence of rare events, and also create counterfactual scenarios described by the time series. Distributional-similarity (which we refer to as realism) as well as the satisfaction of certain numerical constraints are common requirements in counterfactual time series scenario generation requests. For instance, the US Federal Reserve publishes synthetic market stress scenarios given by the constrained time series for financial institutions to assess their performance in hypothetical recessions. Existing approaches for generating constrained time series usually penalize training loss to enforce constraints, and reject non-conforming samples. However, these approaches would require re-training if we change constraints, and rejection sampling can be computationally expensive, or impractical for complex constraints. In this paper, we propose a novel set of methods to tackle the constrained time series generation problem and provide efficient sampling while ensuring the realism of generated time series. In particular, we frame the problem using a constrained optimization framework and then we propose a set of generative methods including "GuidedDiffTime", a guided diffusion model to generate realistic time series. Empirically, we evaluate our work on several datasets for financial and energy data, where incorporating constraints is critical. We show that our approaches outperform existing work both qualitatively and quantitatively. Most importantly, we show that our "GuidedDiffTime" model is the only solution where re-training is not necessary for new constraints, resulting in a significant carbon footprint reduction, up to 92% w.r.t. existing deep learning methods.