# Deep Latent State Space Models for Time-Series Generation

arXiv: https://arxiv.org/abs/2212.12749 · HTML: https://mlsanity.com/paper/2212.12749/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Placed in Time series forecasting with SSMs, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 38 of its 58 references that are in the map.
- First posted on arXiv 24 Dec 2022.

## Placed in

- State-space sequence models (S4, Mamba) / [Time series forecasting with SSMs](https://mlsanity.com/ssm/time-series-forecasting-with-ssms/)

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Generating Videos with Dynamics-aware Implicit Generative Adversarial Networks](https://mlsanity.com/paper/2202.10571/) (2022)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Generating Long Videos of Dynamic Scenes](https://mlsanity.com/paper/2206.03429/) (2022)
- [Stochastic Latent Residual Video Prediction](https://mlsanity.com/paper/2002.09219/) (2020)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)

## Built on by (most cited first, 30 of 38)

- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Simple Hardware-Efficient Long Convolutions for Sequence Modeling](https://mlsanity.com/paper/2302.06646/) (2023)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs](https://mlsanity.com/paper/2310.02619/) (2023)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Facing Off World Model Backbones: RNNs, Transformers, and S4](https://mlsanity.com/paper/2307.02064/) (2023)
- [CodeBrain: Bridging Decoupled Tokenizer and Multi-Scale Architecture for EEG Foundation Model](https://mlsanity.com/paper/2506.09110/) (2025)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [Slot State Space Models](https://mlsanity.com/paper/2406.12272/) (2024)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [Conditional Generators for Limit Order Book Environments: Explainability, Challenges, and Robustness](https://mlsanity.com/paper/2306.12806/) (2023)
- [Revisiting Structured Variational Autoencoders](https://mlsanity.com/paper/2305.16543/) (2023)
- [KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertainty](https://mlsanity.com/paper/2406.15131/) (2024)
- [Forging Time Series with Language: A Large Language Model Approach to Synthetic Data Generation](https://mlsanity.com/paper/2505.17103/) (2025)
- [Deep Bayesian Filter for Bayes-faithful Data Assimilation](https://mlsanity.com/paper/2405.18674/) (2024)
- [TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generation](https://mlsanity.com/paper/2408.06672/) (2024)
- [Sequential Order-Robust Mamba for Time Series Forecasting](https://mlsanity.com/paper/2410.23356/) (2024)
- [Representation Learning For Efficient Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2406.02890/) (2024)
- [Parallelizing Autoregressive Generation with Variational State Space Models](https://mlsanity.com/paper/2407.08415/) (2024)
- [CENTS: Generating synthetic electricity consumption time series for rare and unseen scenarios](https://mlsanity.com/paper/2501.14426/) (2025)
- [A Deep State Space Model for Rainfall-Runoff Simulations](https://mlsanity.com/paper/2501.14980/) (2025)
- [CTBench: Cryptocurrency Time Series Generation Benchmark](https://mlsanity.com/paper/2508.02758/) (2025)
- [Neural Stochastic Differential Equations with Change Points: A Generative Adversarial Approach](https://mlsanity.com/paper/2312.13152/) (2023)
- [DS-Diffusion: Data Style-Guided Diffusion Model for Time-Series Generation](https://mlsanity.com/paper/2509.18584/) (2025)
- [Sequence Modeling with Spectral Mean Flows](https://mlsanity.com/paper/2510.15366/) (2025)
- [TSGDiff: Rethinking Synthetic Time Series Generation from a Pure Graph Perspective](https://mlsanity.com/paper/2511.12174/) (2025)
- [MOSAIC: Modular Orchestration for Structured Agentic Intelligence and Composition](https://mlsanity.com/paper/2606.00708/) (2026)
- [Variational Neural Stochastic Differential Equations with Change Points](https://mlsanity.com/paper/2411.00635/) (2024)
- [WDformer: A Wavelet-based Differential Transformer Model for Time Series Forecasting](https://mlsanity.com/paper/2509.25231/) (2025)

## Abstract (arXiv)

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.