# Latent Abstractions in Generative Diffusion Models

arXiv: https://arxiv.org/abs/2410.03368 · HTML: https://mlsanity.com/paper/2410.03368/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 71 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Diffusion Models already have a Semantic Latent Space](https://mlsanity.com/paper/2210.10960/) (2022)
- [Experience Grounds Language](https://mlsanity.com/paper/2004.10151/) (2020)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [DiffusionBERT: Improving Generative Masked Language Models with Diffusion Models](https://mlsanity.com/paper/2211.15029/) (2022)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [DiffSinger: Singing Voice Synthesis via Shallow Diffusion Mechanism](https://mlsanity.com/paper/2105.02446/) (2021)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [Denoising Diffusion Autoencoders are Unified Self-supervised Learners](https://mlsanity.com/paper/2303.09769/) (2023)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Improved sampling via learned diffusions](https://mlsanity.com/paper/2307.01198/) (2023)
- [A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data](https://mlsanity.com/paper/2402.16991/) (2024)

## Built on by (most cited first, 4 of 4)

- [Entropic Time Schedulers for Generative Diffusion Models](https://mlsanity.com/paper/2504.13612/) (2025)
- [The Information Dynamics of Generative Diffusion](https://mlsanity.com/paper/2508.19897/) (2025)
- [Latent Structure Emergence in Diffusion Models via Confidence-Based Filtering](https://mlsanity.com/paper/2602.06155/) (2026)
- [Towards Diverse and Comprehensive Benchmarks for Mutual Information Estimation](https://mlsanity.com/paper/2607.03487/) (2026)

## Abstract (arXiv)

In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We present a novel theoretical framework that extends NLF, and that offers a unique perspective on SDE-based generative models. The development of our theory relies on a novel formulation of the joint (state and measurement) dynamics, and an information-theoretic measure of the influence of the system state on the measurement process. According to our theory, diffusion models can be cast as a system of SDE, describing a non-linear filter in which the evolution of unobservable latent abstractions steers the dynamics of an observable measurement process (corresponding to the generative pathways). In addition, we present an empirical study to validate our theory and previous empirical results on the emergence of latent abstractions at different stages of the generative process.