# Efficient Learning of Deep State Space Models via Importance Smoothing

arXiv: https://arxiv.org/abs/2605.21108 · HTML: https://mlsanity.com/paper/2605.21108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 63 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Filtering Variational Objectives](https://mlsanity.com/paper/1705.09279/) (2017)
- [Auto-Encoding Sequential Monte Carlo](https://mlsanity.com/paper/1705.10306/) (2017)
- [Particle Filter Networks with Application to Visual Localization](https://mlsanity.com/paper/1805.08975/) (2018)
- [Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors](https://mlsanity.com/paper/1805.11122/) (2018)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Temporal Parallelization of Bayesian Smoothers](https://mlsanity.com/paper/1905.13002/) (2019)
- [Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2102.00397/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)
- [Revisiting Structured Variational Autoencoders](https://mlsanity.com/paper/2305.16543/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Time-Causal VAE: Robust Financial Time Series Generator](https://mlsanity.com/paper/2411.02947/) (2024)
- [New Money: A Systematic Review of Synthetic Data Generation for Finance](https://mlsanity.com/paper/2510.26076/) (2025)
- [Deep Learning-based Approaches for State Space Models: A Selective Review](https://mlsanity.com/paper/2412.11211/) (2024)
- [Learning to be Smooth: An End-to-End Differentiable Particle Smoother](https://mlsanity.com/paper/2502.10546/) (2025)
- [De-Sequentialized Monte Carlo: a parallel-in-time particle smoother](https://mlsanity.com/paper/2202.02264/) (2022)
- [PyDPF: A Python Package for Differentiable Particle Filtering](https://mlsanity.com/paper/2510.25693/) (2025)
- [Diffusion differentiable resampling](https://mlsanity.com/paper/2512.10401/) (2025)

## Abstract (arXiv)

Latent state space systems are ubiquitous in statistical modelling, arising naturally when time series are observed through noisy measurements. However, training deep state space models (DSSMs) at scale remains difficult. Two largely distinct strategies have emerged for training DSSMs. The first, auto-encoding DSSMs, trains generative models by optimising a variational lower bound. The second backpropagates through the outputs of classical sequential Monte Carlo (SMC) algorithms. Such approaches can train DSSMs for both discriminative and generative tasks, but their inherently sequential forward passes scale poorly on modern hardware. We propose parallel variational Monte Carlo (PVMC), a new training method that bridges these paradigms and robustly trains DSSMs for both discriminative and generative tasks. Across a set of benchmark experiments, PVMC matches or exceeds state-of-the-art performance while training 10× faster than the fastest competing SMC-based approach.