# Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2307.11494 · HTML: https://mlsanity.com/paper/2307.11494/

## Key facts

- Cited by 88 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 37 of its 57 references that are in the map.
- First posted on arXiv 21 Jul 2023.

## 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 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [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)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)

## Built on by (most cited first, 30 of 88)

- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [Gradient-Free Generation for Hard-Constrained Systems](https://mlsanity.com/paper/2412.01786/) (2024)
- [TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Model](https://mlsanity.com/paper/2409.02322/) (2024)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [TacDiffusion: Force-domain Diffusion Policy for Precise Tactile Manipulation](https://mlsanity.com/paper/2409.11047/) (2024)
- [FlowTS: Time Series Generation via Rectified Flow](https://mlsanity.com/paper/2411.07506/) (2024)
- [A Survey on Diffusion Models for Recommender Systems](https://mlsanity.com/paper/2409.05033/) (2024)
- [BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modeling](https://mlsanity.com/paper/2503.02445/) (2025)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2501.13989/) (2025)
- [ANT: Adaptive Noise Schedule for Time Series Diffusion Models](https://mlsanity.com/paper/2410.14488/) (2024)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [Diffusion Transformers as Open-World Spatiotemporal Foundation Models](https://mlsanity.com/paper/2411.12164/) (2024)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [Unified Guidance for Geometry-Conditioned Molecular Generation](https://mlsanity.com/paper/2501.02526/) (2025)
- [Vision-Enhanced Time Series Forecasting via Latent Diffusion Models](https://mlsanity.com/paper/2502.14887/) (2025)
- [Probabilistic Forecasting via Autoregressive Flow Matching](https://mlsanity.com/paper/2503.10375/) (2025)
- [Towards Identifiability of Hierarchical Temporal Causal Representation Learning](https://mlsanity.com/paper/2510.18310/) (2025)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [Constrained Posterior Sampling: Time Series Generation with Hard Constraints](https://mlsanity.com/paper/2410.12652/) (2024)
- [Assessing Robustness via Score-Based Adversarial Image Generation](https://mlsanity.com/paper/2310.04285/) (2023)
- [Generative Semantic Communication: Architectures, Technologies, and Applications](https://mlsanity.com/paper/2412.08642/) (2024)
- [Byte Pair Encoding for Efficient Time Series Forecasting](https://mlsanity.com/paper/2505.14411/) (2025)
- [Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching](https://mlsanity.com/paper/2507.07192/) (2025)
- [Unfolding Time: Generative Modeling for Turbulent Flows in 4D](https://mlsanity.com/paper/2406.11390/) (2024)

## Abstract (arXiv)

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).