# Lecture Notes in Probabilistic Diffusion Models

arXiv: https://arxiv.org/abs/2312.10393 · HTML: https://mlsanity.com/paper/2312.10393/

## 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 16 of its 18 references that are in the map.
- First posted on arXiv 16 Dec 2023.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [A Survey on Video Diffusion Models](https://mlsanity.com/paper/2310.10647/) (2023)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [Bayesian Flow Networks](https://mlsanity.com/paper/2308.07037/) (2023)

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

- [Evolutionary Computation as Natural Generative AI](https://mlsanity.com/paper/2510.08590/) (2025)

## Abstract (arXiv)

Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where textitdiffusion refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite similar, namely the process of transforming a complex distribution pcomplex on ℝd to a simple distribution pprior on the same domain. This constitutes a Markov chain of diffusion steps of slowly adding random noise to data, followed by a reverse diffusion process in which the data is reconstructed from the noise. The diffusion model learns the data manifold to which the original and thus the reconstructed data samples belong, by training on a large number of data points. While the diffusion process pushes a data sample off the data manifold, the reverse process finds a trajectory back to the data manifold. Diffusion models have -- unlike variational autoencoder and flow models -- latent variables with the same dimensionality as the original data, and they are currentlyfootnoteAt the time of writing, 2023. outperforming other approaches -- including Generative Adversarial Networks (GANs) -- to modelling the distribution of, e.g., natural images.