# Non-stationary Diffusion For Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2505.04278 · HTML: https://mlsanity.com/paper/2505.04278/

## Key facts

- Cited by 27 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 29 of its 46 references that are in the map.
- First posted on arXiv 7 May 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, 29 of 29)

- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [Training neural operators to preserve invariant measures of chaotic attractors](https://mlsanity.com/paper/2306.01187/) (2023)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [DDG-DA: Data Distribution Generation for Predictable Concept Drift Adaptation](https://mlsanity.com/paper/2201.04038/) (2022)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)
- [Deep Frequency Derivative Learning for Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2407.00502/) (2024)
- [Ordering-Based Causal Discovery for Linear and Nonlinear Relations](https://mlsanity.com/paper/2410.05890/) (2024)
- [ANT: Adaptive Noise Schedule for Time Series Diffusion Models](https://mlsanity.com/paper/2410.14488/) (2024)

## Built on by (most cited first, 27 of 27)

- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [EventTSF: Event-Aware Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2508.13434/) (2025)
- [StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser](https://mlsanity.com/paper/2603.00037/) (2026)
- [ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusion](https://mlsanity.com/paper/2609.37078/) (2026)
- [Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.20928/) (2025)
- [CoGenCast: A Coupled Autoregressive-Flow Generative Framework for Time Series Forecasting](https://mlsanity.com/paper/2602.03564/) (2026)
- [DECODE: Dual-Enhanced Conditioned Diffusion for EEG Forecasting](https://mlsanity.com/paper/2603.16885/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2603.24254/) (2026)
- [SURGE: An Event-Centric Social Media Sentiment Time Series Benchmark with Interaction Structure](https://mlsanity.com/paper/2605.21198/) (2026)
- [Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2605.23402/) (2026)
- [ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2606.02117/) (2026)
- [StrideDiffusion: Accelerating Diffusion Models for Time-series Generation](https://mlsanity.com/paper/2607.20545/) (2026)
- [Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting](https://mlsanity.com/paper/2607.22599/) (2026)
- [Evaluating Generative Time-Series Models on Data with Point Masses](https://mlsanity.com/paper/2608.09692/) (2026)
- [SCENARIODIFF: A Scenario-level Guidance Framework for Multimodal Time Series Forecasting--Extended Version](https://mlsanity.com/paper/2608.17164/) (2026)
- [SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2608.17333/) (2026)
- [DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2609.32363/) (2026)
- [TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra](https://mlsanity.com/paper/2609.32384/) (2026)
- [KiT: A Foundation Model for Financial Time-Series Forecasting using DiffusionTransformers](https://mlsanity.com/paper/2609.34507/) (2026)
- [Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolios](https://mlsanity.com/paper/2609.35086/) (2026)
- [GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2609.37694/) (2026)
- [ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.01320/) (2026)
- [NV-Tesseract-AD: Curriculum-Enhanced Conditional Diffusion for Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2610.12754/) (2026)
- [Deterministic Prediction as Global Velocity: Flow Matching for Probabilistic Time-Series Forecast](https://mlsanity.com/paper/2610.18621/) (2026)

## Abstract (arXiv)

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.