Diffusion-Driven State Space Models
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.
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BibTeX
@misc{ruder2026diffusiondriven,
title = {{Diffusion-Driven State Space Models}},
author = {Jack Ruder and Michael Wojnowicz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.21036},
eprint = {2606.21036},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21036},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diffusion-Driven State Space Models
AU - Jack Ruder
AU - Michael Wojnowicz
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2606.21036
UR - https://arxiv.org/abs/2606.21036
AB - 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.
ER -