DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting

2026-09-26

AI Summary

This study addresses the fragmented training objectives and distribution shift inherent in diffusion models for probabilistic time series forecasting. We propose a unified end-to-end optimization framework that reconstructs the evidence lower bound (ELBO) using a location-scale noise model (LSNM). By deriving a Gaussian negative log-likelihood objective, our approach integrates mean-variance estimation and variational inference within a single diffusion paradigm, fundamentally resolving the theoretical limitations of existing methods. The proposed framework achieves state-of-the-art performance across multiple benchmarks, reducing the Continuous Ranked Probability Score (CRPS) and Mean Squared Error (MSE) by an average of 14.53% and 16.55%, respectively, compared to current approaches. This work provides a principled solution for probabilistic time series forecasting.

Abstract

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.

Problem

• Probabilistic Time Series Forecasting
• Denoising Diffusion Probabilistic Model
• Evidence Lower Bound
• Location-Scale Noise Model

Innovation

• Probabilistic Time Series Forecasting
• Diffusion Models
• Evidence Lower Bound (ELBO)
• Location-Scale Noise Model
• End-to-End Optimization