# A Study of Posterior Stability for Time-Series Latent Diffusion

arXiv: https://arxiv.org/abs/2405.14021 · HTML: https://mlsanity.com/paper/2405.14021/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 22 May 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Snips Voice Platform: an embedded Spoken Language Understanding system for private-by-design voice interfaces](https://mlsanity.com/paper/1805.10190/) (2018)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [Avoiding Latent Variable Collapse With Generative Skip Models](https://mlsanity.com/paper/1807.04863/) (2018)
- [A Hybrid Convolutional Variational Autoencoder for Text Generation](https://mlsanity.com/paper/1702.02390/) (2017)
- [Personalized Risk Scoring for Critical Care Prognosis using Mixtures of Gaussian Processes](https://mlsanity.com/paper/1610.08853/) (2016)
- [Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosis](https://mlsanity.com/paper/1705.05267/) (2017)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Auto-Encoding Variational Neural Machine Translation](https://mlsanity.com/paper/1807.10564/) (2018)
- [TS-Diffusion: Generating Highly Complex Time Series with Diffusion Models](https://mlsanity.com/paper/2311.03303/) (2023)
- [Soft Mixture Denoising: Beyond the Expressive Bottleneck of Diffusion Models](https://mlsanity.com/paper/2309.14068/) (2023)

## Built on by (most cited first, 1 of 1)

- [Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models](https://mlsanity.com/paper/2506.20771/) (2025)

## Abstract (arXiv)

Latent diffusion has demonstrated promising results in image generation and permits efficient sampling. However, this framework might suffer from the problem of posterior collapse when applied to time series. In this paper, we first show that posterior collapse will reduce latent diffusion to a variational autoencoder (VAE), making it less expressive. This highlights the importance of addressing this issue. We then introduce a principled method: dependency measure, that quantifies the sensitivity of a recurrent decoder to input variables. Using this tool, we confirm that posterior collapse significantly affects time-series latent diffusion on real datasets, and a phenomenon termed dependency illusion is also discovered in the case of shuffled time series. Finally, building on our theoretical and empirical studies, we introduce a new framework that extends latent diffusion and has a stable posterior. Extensive experiments on multiple real time-series datasets show that our new framework is free from posterior collapse and significantly outperforms previous baselines in time series synthesis.