Diffusion-Driven State Space Models

Jack Ruder, Michael Wojnowicz

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.

Keywords: state, space, model, models, diffusion, prior, time, series, latent, dvae, dssm, ssm, dynamical

TLDR: State-Space Models made expressive via diffusion-based transitions.

Submission Number: 20