# WaveStitch: Flexible and Fast Conditional Time Series Generation with Diffusion Models

arXiv: https://arxiv.org/abs/2503.06231 · HTML: https://mlsanity.com/paper/2503.06231/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 38 of its 62 references that are in the map.
- First posted on arXiv 8 Mar 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Video Probabilistic Diffusion Models in Projected Latent Space](https://mlsanity.com/paper/2302.07685/) (2023)
- [NUWA-XL: Diffusion over Diffusion for eXtremely Long Video Generation](https://mlsanity.com/paper/2303.12346/) (2023)
- [Make Pixels Dance: High-Dynamic Video Generation](https://mlsanity.com/paper/2311.10982/) (2023)
- [On The Computational Complexity of Self-Attention](https://mlsanity.com/paper/2209.04881/) (2022)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Gradient Inversion with Generative Image Prior](https://mlsanity.com/paper/2110.14962/) (2021)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Beyond One-hot Encoding: lower dimensional target embedding](https://mlsanity.com/paper/1806.10805/) (2018)

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

- [Detecting Diffusion-Generated Time Series Under Generator Shift](https://mlsanity.com/paper/2605.28355/) (2026)
- [Represent, Then Generate: Multimodal-Conditioned Time-Series Generation under Irregular Missingness](https://mlsanity.com/paper/2608.12592/) (2026)
- [GALA: Generation-Aware Cross-Modal Alignment for Text-to-Time-Series Synthesis](https://mlsanity.com/paper/2608.13741/) (2026)
- [CodeTS: Verifiable Text-to-Time Series Generation via Executable Code](https://mlsanity.com/paper/2609.15393/) (2026)

## Abstract (arXiv)

Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face three key limitations: (1) they condition on either the metadata or observed values, but rarely both together; (2) they adopt either training-time approaches that fail to generalize to unseen scenarios, or inference-time approaches that ignore metadata; and (3) they suffer from trade-offs between generation speed and temporal coherence across time windows--choosing either slow but coherent autoregressive methods or fast but incoherent parallel ones. We propose WaveStitch, a novel diffusion-based method to overcome these hurdles through: (1) dual-sourced conditioning on both metadata and partially observed signals; (2) a hybrid training-inference architecture, incorporating metadata during training and observations at inference via gradient-based guidance; and (3) a novel pipeline-style paradigm that generates time windows in parallel while preserving coherence through an inference-time conditional loss and a stitching mechanism. Across diverse datasets, WaveStitch demonstrates adaptability to arbitrary patterns of observed signals, achieving 1.81x lower mean-squared-error compared to the state-of-the-art, and generates data up to 166.48x faster than autoregressive methods while maintaining coherence. Our code is available at: https://github.com/adis98/WaveStitch