# ANT: Adaptive Noise Schedule for Time Series Diffusion Models

arXiv: https://arxiv.org/abs/2410.14488 · HTML: https://mlsanity.com/paper/2410.14488/

## Key facts

- Cited by 11 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 24 of its 40 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## 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, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [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)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [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)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [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)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process](https://mlsanity.com/paper/2403.05751/) (2024)

## Built on by (most cited first, 11 of 11)

- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [MRI super-resolution reconstruction using efficient diffusion probabilistic model with residual shifting](https://mlsanity.com/paper/2503.01576/) (2025)
- [Exploring Diffusion and Flow Matching Under Generator Matching](https://mlsanity.com/paper/2412.11024/) (2024)
- [Theoretical Foundation of Flow-Based Time Series Generation: Provable Approximation, Generalization, and Efficiency](https://mlsanity.com/paper/2503.14076/) (2025)
- [DS-Diffusion: Data Style-Guided Diffusion Model for Time-Series Generation](https://mlsanity.com/paper/2509.18584/) (2025)
- [StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser](https://mlsanity.com/paper/2603.00037/) (2026)
- [Alternators With Noise Models](https://mlsanity.com/paper/2505.12544/) (2025)
- [Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2605.23402/) (2026)
- [Towards a Unified Generative Model for Scarce Time Series with Domain Experts](https://mlsanity.com/paper/2606.15172/) (2026)
- [When Denoising Hurts: Rethinking the Terminal Step of Diffusion Time Series Forecasters -- Extended Version](https://mlsanity.com/paper/2608.14067/) (2026)
- [EXAONE Demand 1.0: A Time Series Foundation Model for Demand Forecasting](https://mlsanity.com/paper/2609.30880/) (2026)

## Abstract (arXiv)

Advances in diffusion models for generative artificial intelligence have recently propagated to the time series (TS) domain, demonstrating state-of-the-art performance on various tasks. However, prior works on TS diffusion models often borrow the framework of existing works proposed in other domains without considering the characteristics of TS data, leading to suboptimal performance. In this work, we propose Adaptive Noise schedule for Time series diffusion models (ANT), which automatically predetermines proper noise schedules for given TS datasets based on their statistics representing non-stationarity. Our intuition is that an optimal noise schedule should satisfy the following desiderata: 1) It linearly reduces the non-stationarity of TS data so that all diffusion steps are equally meaningful, 2) the data is corrupted to the random noise at the final step, and 3) the number of steps is sufficiently large. The proposed method is practical for use in that it eliminates the necessity of finding the optimal noise schedule with a small additional cost to compute the statistics for given datasets, which can be done offline before training. We validate the effectiveness of our method across various tasks, including TS forecasting, refinement, and generation, on datasets from diverse domains. Code is available at this repository: https://github.com/seunghan96/ANT.