# Latent Dynamical Implicit Diffusion Processes

arXiv: https://arxiv.org/abs/2306.07077 · HTML: https://mlsanity.com/paper/2306.07077/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using Householder Reflections](https://mlsanity.com/paper/1612.00188/) (2016)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [Deep Learning Techniques for Music Generation -- A Survey](https://mlsanity.com/paper/1709.01620/) (2017)
- [Machine learning for neural decoding](https://mlsanity.com/paper/1708.00909/) (2017)
- [Improving Variational Auto-Encoders using Householder Flow](https://mlsanity.com/paper/1611.09630/) (2016)
- [Linear dynamical neural population models through nonlinear embeddings](https://mlsanity.com/paper/1605.08454/) (2016)
- [Black box variational inference for state space models](https://mlsanity.com/paper/1511.07367/) (2015)
- [Reverse Survival Model (RSM): A Pipeline for Explaining Predictions of Deep Survival Models](https://mlsanity.com/paper/2210.15674/) (2022)

## Abstract (arXiv)

Latent dynamical models are commonly used to learn the distribution of a latent dynamical process that represents a sequence of noisy data samples. However, producing samples from such models with high fidelity is challenging due to the complexity and variability of latent and observation dynamics. Recent advances in diffusion-based generative models, such as DDPM and NCSN, have shown promising alternatives to state-of-the-art latent generative models, such as Neural ODEs, RNNs, and Normalizing flow networks, for generating high-quality sequential samples from a prior distribution. However, their application in modeling sequential data with latent dynamical models is yet to be explored. Here, we propose a novel latent variable model named latent dynamical implicit diffusion processes (LDIDPs), which utilizes implicit diffusion processes to sample from dynamical latent processes and generate sequential observation samples accordingly. We tested LDIDPs on synthetic and simulated neural decoding problems. We demonstrate that LDIDPs can accurately learn the dynamics over latent dimensions. Furthermore, the implicit sampling method allows for the computationally efficient generation of high-quality sequential data samples from the latent and observation spaces.