Diffusion-Driven State Space Models
Jack Ruder, Michael Wojnowicz
stat.ML, cs.LG
Submitted: 2026-06-19
Comments: Accepted to ProbML 2026 Workshop Track
License: http://creativecommons.org/licenses/by/4.0/
The gist: In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics.
Terminology
Abstract
In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.
Sources
- Training Deep Nets with Sublinear Memory Cost
- Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data
- Deep Kalman Filters
- Auto-Encoding Sequential Monte Carlo
- TimeLDM: Latent Diffusion Model for Unconditional Time Series Generation
- Taming VAEs
- Score-Based Generative Modeling through Stochastic Differential Equations
- Diffusion Models for Time Series Forecasting: A Survey
Related papers
- Behavior of prediction performance metrics with rare events
- Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
- A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
- Scalable Posterior Uncertainty for Flexible Density-Based Clustering
- A Transport Geometry of Benign Overfitting
- Efficient quadratic entropy with distance sketches