# Regular Time-series Generation using SGM

arXiv: https://arxiv.org/abs/2301.08518 · HTML: https://mlsanity.com/paper/2301.08518/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 20 Jan 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [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)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [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)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [SOS: Score-based Oversampling for Tabular Data](https://mlsanity.com/paper/2206.08555/) (2022)
- [Smoothness and Stability in GANs](https://mlsanity.com/paper/2002.04185/) (2020)

## Built on by (most cited first, 23 of 23)

- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2307.00754/) (2023)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [FlowTS: Time Series Generation via Rectified Flow](https://mlsanity.com/paper/2411.07506/) (2024)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [Efficiently Parameterized Neural Metriplectic Systems](https://mlsanity.com/paper/2405.16305/) (2024)
- [A Comprehensive Survey on Generative Diffusion Models for Structured Data](https://mlsanity.com/paper/2306.04139/) (2023)
- [Navigating Tabular Data Synthesis Research: Understanding User Needs and Tool Capabilities](https://mlsanity.com/paper/2405.20959/) (2024)
- [Robust time series generation via Schr"odinger Bridge: a comprehensive evaluation](https://mlsanity.com/paper/2503.02943/) (2025)
- [Modeling Human Gaze Behavior with Diffusion Models for Unified Scanpath Prediction](https://mlsanity.com/paper/2507.23021/) (2025)
- [TRADES: Generating Realistic Market Simulations with Diffusion Models](https://mlsanity.com/paper/2502.07071/) (2025)
- [Alternators For Sequence Modeling](https://mlsanity.com/paper/2405.11848/) (2024)
- [TimeWak: Temporal Chained-Hashing Watermark for Time Series Data](https://mlsanity.com/paper/2506.06407/) (2025)
- [CTBench: Cryptocurrency Time Series Generation Benchmark](https://mlsanity.com/paper/2508.02758/) (2025)
- [WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation](https://mlsanity.com/paper/2510.11839/) (2025)
- [MadSGM: Multivariate Anomaly Detection with Score-based Generative Models](https://mlsanity.com/paper/2308.15069/) (2023)
- [Text2Data: Low-Resource Data Generation with Textual Control](https://mlsanity.com/paper/2402.10941/) (2024)
- [Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models](https://mlsanity.com/paper/2602.17830/) (2026)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)
- [Unconditional flow-based time series generation with equivariance-regularised latent spaces](https://mlsanity.com/paper/2601.22848/) (2026)
- [High-Quality Synthetic Financial Time-Series using a GAN-Diffusion Framework](https://mlsanity.com/paper/2605.27113/) (2026)
- [Time series generation with spectrally aligned latent flow matching](https://mlsanity.com/paper/2609.21989/) (2026)

## Abstract (arXiv)

Score-based generative models (SGMs) are generative models that are in the spotlight these days. Time-series frequently occurs in our daily life, e.g., stock data, climate data, and so on. Especially, time-series forecasting and classification are popular research topics in the field of machine learning. SGMs are also known for outperforming other generative models. As a result, we apply SGMs to synthesize time-series data by learning conditional score functions. We propose a conditional score network for the time-series generation domain. Furthermore, we also derive the loss function between the score matching and the denoising score matching in the time-series generation domain. Finally, we achieve state-of-the-art results on real-world datasets in terms of sampling diversity and quality.