mlsanityData to 7 Oct 2026

Diffusion-Driven State Space Models

arXiv 2606.21036 ↗First posted 19 Jun 2026stat.ML cs.LGcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 34 of its 54 references that are in the map. First posted on arXiv 19 Jun 2026.

Builds on

34 of 54 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025Diffusion Models for Time Series Forecasting: A Survey19 Jul
  2. 2024TimeLDM: Latent Diffusion Model for Unconditional Time Series Generation5 Jul
  3. 2024TimeAutoDiff: A Unified Framework for Generation, Imputation, Forecasting, and Time-Varying Metadata Conditioning of Heterogeneous Time Series Tabular Data23 Jun
  4. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting21 Jul
  5. 2023End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics17 May
  6. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
  7. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan

Other references · 27

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  6. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  7. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  8. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  9. 2016Training Deep Nets with Sublinear Memory Costcited by 825
  10. 2021Score-based Generative Modeling in Latent Spacecited by 634
  11. 2017VAE with a VampPriorcited by 247
  12. 2016Structured Inference Networks for Nonlinear State Space Modelscited by 182
15 more
  1. 2016Variational Lossy Autoencodercited by 175
  2. 2015Deep Kalman Filterscited by 163
  3. 2016Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Datacited by 154
  4. 2021KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamicscited by 128
  5. 2020Dynamical Variational Autoencoders: A Comprehensive Reviewcited by 127
  6. 2016Composing graphical models with neural networks for structured representations and fast inferencecited by 113
  7. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  8. 2018Taming VAEscited by 85
  9. 2019Latent Normalizing Flows for Discrete Sequencescited by 66
  10. 2017Auto-Encoding Sequential Monte Carlocited by 64
  11. 2019Learning Hierarchical Priors in VAEscited by 53
  12. 2021Deep Explicit Duration Switching Models for Time Seriescited by 17
  13. 2024Normalizing Flow-based Differentiable Particle Filterscited by 10
  14. 2024eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modelingcited by 7
  15. 2026Latent Matters: Learning Deep State-Space Modelscited by 2

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  1. 2023Diffusion Models for Time Series Applications: A Survey
  2. 2024The Rise of Diffusion Models in Time-Series Forecasting
  3. 2026Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting
  4. 2022Deep Latent State Space Models for Time-Series Generation
  5. 2023Effectively Modeling Time Series with Simple Discrete State Spaces
  6. 2026Discrete Diffusion Models: A Unified Framework from Tokenization to Generation
  7. 2026Enhancing few-shot time series forecasting with LLM-guided diffusion
  8. 2024Deep Learning-based Approaches for State Space Models: A Selective Review