# Sequential Posterior Sampling with Diffusion Models

arXiv: https://arxiv.org/abs/2409.05399 · HTML: https://mlsanity.com/paper/2409.05399/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 21 of 21)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Conditional Image-to-Video Generation with Latent Flow Diffusion Models](https://mlsanity.com/paper/2303.13744/) (2023)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [Experimental design for MRI by greedy policy search](https://mlsanity.com/paper/2010.16262/) (2020)
- [Echo from noise: synthetic ultrasound image generation using diffusion models for real image segmentation](https://mlsanity.com/paper/2305.05424/) (2023)
- [Dehazing Ultrasound using Diffusion Models](https://mlsanity.com/paper/2307.11204/) (2023)
- [Learning Sub-Sampling and Signal Recovery with Applications in Ultrasound Imaging](https://mlsanity.com/paper/1908.05764/) (2019)
- [Active Diffusion Subsampling](https://mlsanity.com/paper/2406.14388/) (2024)
- [Image reconstruction in dynamic inverse problems with temporal models](https://mlsanity.com/paper/2007.10238/) (2020)
- [Accelerated Intravascular Ultrasound Imaging using Deep Reinforcement Learning](https://mlsanity.com/paper/2201.09522/) (2022)

## Built on by (most cited first, 7 of 7)

- [Particle-Guided Diffusion Models for Partial Differential Equations](https://mlsanity.com/paper/2601.23262/) (2026)
- [High Volume Rate 3D Ultrasound Reconstruction with Diffusion Models](https://mlsanity.com/paper/2505.22090/) (2025)
- [A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios](https://mlsanity.com/paper/2512.23748/) (2025)
- [Heat Diffusion Models -- Interpixel Attention Mechanism](https://mlsanity.com/paper/2504.19600/) (2025)
- [Nuclear Diffusion Models for Low-Rank Background Suppression in Videos](https://mlsanity.com/paper/2509.20886/) (2025)
- [Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Sampling](https://mlsanity.com/paper/2604.16461/) (2026)
- [Deep Bayesian REFoCUS](https://mlsanity.com/paper/2610.03419/) (2026)

## Abstract (arXiv)

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive and unsuitable for real-time sequential inverse problems such as ultrasound imaging. Considering the strong temporal structure across sequences of frames, we propose a novel approach that models the transition dynamics to improve the efficiency of sequential diffusion posterior sampling in conditional image synthesis. Through modeling sequence data using a video vision transformer (ViViT) transition model based on previous diffusion outputs, we can initialize the reverse diffusion trajectory at a lower noise scale, greatly reducing the number of iterations required for convergence. We demonstrate the effectiveness of our approach on a real-world dataset of high frame rate cardiac ultrasound images and show that it achieves the same performance as a full diffusion trajectory while accelerating inference 25×, enabling real-time posterior sampling. Furthermore, we show that the addition of a transition model improves the PSNR up to 8% in cases with severe motion. Our method opens up new possibilities for real-time applications of diffusion models in imaging and other domains requiring real-time inference.