mlsanityData to 14 Oct 2026

DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting

arXiv 2609.32363 ↗First posted 26 Sep 2026cs.LG cs.AIcited by 0

On the map: Diffusion models → Diffusion foundations and sampling also fits: Flow matching, time series and science

Abstract (arXiv)

Probabilistic time series forecasting requires modeling and predicting complex and time-varying distributions. Recently, Denoising Diffusion Probabilistic Model (DDPM)-based approaches have shown promise by equipping the dif- fusion process with pretrained mean and variance estimators to accommodate distributional shift. However, these methods typically follow the standard DDPM framework and consider only partial components of the evidence lower bound (ELBO), treating the training of estimators as designed regression tasks separate from the variational inference framework. To address this, we rethink the ELBO under the Location-Scale Noise Model (LSNM) and find that it naturally induces a Gaussian negative log likelihood objective for the estimators and inherently defines a joint training objective that unifies recent diffusion paradigms for probabilistic forecasting. Building on this principled ELBO reformulation, we propose Diff- PTS, a general framework that enables end-to-end optimization of all components within the ELBO. Across multiple benchmarks, DiffPTS consistently outperforms recent models, achieving state-of-the-art performance with an average CRPS/MSE reduction of over 14.53%/16.55% compared to existing diffusion-based methods. The code is available at https://github.com/wwy155/DiffPTS.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 35 of its 58 references that are in the map. First posted on arXiv 26 Sep 2026.

Builds on

35 of 58 references.

Closest ancestors · 9

Same direction, newest first

  1. 2024Step-by-Step Diffusion: An Elementary Tutorial13 Jun
  2. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  3. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
  4. 2022CARD: Classification and Regression Diffusion Models15 Jun
  5. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  6. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  7. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models6 Aug
  8. 2020Denoising Diffusion Implicit Models6 Oct
  9. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 26

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  3. 2022Generative Adversarial Networkscited by 5,627
  4. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  5. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  6. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 2,039
  7. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,676
  8. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,424
  9. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,058
  10. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  11. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  12. 2020Time Series Forecasting With Deep Learning: A Surveycited by 459
14 more
  1. 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 391
  2. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 337
  3. 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generationcited by 184
  4. 2021TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generationcited by 142
  5. 2021PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Priorcited by 80
  6. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 78
  7. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  8. 2024TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecastingcited by 40
  9. 2025Non-stationary Diffusion For Probabilistic Time Series Forecastingcited by 27
  10. 2023TSGBench: Time Series Generation Benchmarkcited by 26
  11. 2025Diffusion Models for Time Series Forecasting: A Surveycited by 11
  12. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 10
  13. 2025Towards Non-Stationary Time Series Forecasting with Temporal Stabilization and Frequency Differencingcited by 10
  14. 2025RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecastingcited by 4

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