# Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion

arXiv: https://arxiv.org/abs/2505.11306 · HTML: https://mlsanity.com/paper/2505.11306/

## Key facts

- Cited by 3 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 9 of its 55 references that are in the map.
- First posted on arXiv 16 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, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [Open-Sora Plan: Open-Source Large Video Generation Model](https://mlsanity.com/paper/2412.00131/) (2024)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [FLUX-Text: A Simple and Advanced Diffusion Transformer Baseline for Scene Text Editing](https://mlsanity.com/paper/2505.03329/) (2025)
- [USP: Unified Self-Supervised Pretraining for Image Generation and Understanding](https://mlsanity.com/paper/2503.06132/) (2025)
- [Series-to-Series Diffusion Bridge Model](https://mlsanity.com/paper/2411.04491/) (2024)

## Built on by (most cited first, 3 of 3)

- [Diffusion Models for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2507.14507/) (2025)
- [Structured Noise Modeling for Enhanced Time-Series Forecasting](https://mlsanity.com/paper/2511.19657/) (2025)
- [Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting](https://mlsanity.com/paper/2607.22599/) (2026)

## Abstract (arXiv)

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9%.