mlsanityData to 7 Oct 2026

Monotone-Constrained Diffusion Models for Long-Horizon Production Forecasting

arXiv 2609.22643 ↗First posted 18 Sep 2026cs.LG stat.MLcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Forecasting a long horizon from only the first observations of a sequence is ill-posed: many trajectories are consistent with the same short history. We study this problem in oil and gas production forecasting, where forecasts made after roughly the first fifth of a well's producing life drive development and abandonment decisions, and where a usable forecast must describe a monotone decline. We present Physics-SIMS-TS, a conditional diffusion forecaster that combines negative guidance against synthetic artifacts, decline-curve constraints and an isotonic projection applied during sampling, spatial training augmentation, and an ensembled stochastic sampler yielding a full predictive distribution. Across three jurisdictions and more than 35,000 wells, under a shared-space, validation-frozen protocol, Physics-SIMS-TS is the most accurate diffusion forecaster in the comparison and is competitive with, but not superior to, ensembled transformer forecasters. Its forecasts are monotone by construction at a cost of at most 0.5% in mean squared error, and its trajectory ensemble yields calibrated intervals after one dispersion factor is fitted per jurisdiction. On six standard benchmarks a reversible-instance-normalization variant of the backbone is the leading diffusion baseline. We also quantify four protocol choices on which the measured ranking depends. Code and evaluation artifacts are released.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 20 of its 42 references that are in the map. First posted on arXiv 18 Sep 2026.

Builds on

20 of 42 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generation4 Mar
  2. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting21 Jul
  3. 2023Non-autoregressive Conditional Diffusion Models for Time Series Prediction8 Jun
  4. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
  5. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan

Other references · 15

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  4. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
  5. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
  6. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 906
  7. 2024Chronos: Learning the Language of Time Seriescited by 712
  8. 2023Efficient Diffusion Training via Min-SNR Weighting Strategycited by 242
  9. 2023Self-Consuming Generative Models Go MADcited by 239
  10. 2020Time Series Data Augmentation for Deep Learning: A Surveycited by 225
  11. 2025Chronos-2: From Univariate to Universal Forecastingcited by 158
  12. 2021TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generationcited by 139
3 more
  1. 2020An Empirical Survey of Data Augmentation for Time Series Classification with Neural Networkscited by 128
  2. 2024Self-Improving Diffusion Models with Synthetic Datacited by 34
  3. 2023TSGBench: Time Series Generation Benchmarkcited by 24

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2026When Denoising Hurts: Rethinking the Terminal Step of Diffusion Time Series Forecasters -- Extended Version
  2. 2026Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting
  3. 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting
  4. 2025Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics
  5. 2026PDE-regularized Dynamics-informed Diffusion with Uncertainty-aware Filtering for Long-Horizon Dynamics
  6. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting
  7. 2025Semantically-Guided Inference for Conditional Diffusion Models: Enhancing Covariate Consistency in Time Series Forecasting
  8. 2025ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes