# Deep generative models as the probability transformation functions

arXiv: https://arxiv.org/abs/2506.17171 · HTML: https://mlsanity.com/paper/2506.17171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [On Decoding Strategies for Neural Text Generators](https://mlsanity.com/paper/2203.15721/) (2022)
- [Autoregressive Models in Vision: A Survey](https://mlsanity.com/paper/2411.05902/) (2024)
- [Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art](https://mlsanity.com/paper/2308.16316/) (2023)
- [Generative Adversarial Networks for Malware Detection: a Survey](https://mlsanity.com/paper/2302.08558/) (2023)

## Built on by (most cited first, 2 of 2)

- [FlowECG: Using Flow Matching to Create a More Efficient ECG Signal Generator](https://mlsanity.com/paper/2509.10491/) (2025)
- [Velocity Scheduled Flow Matching](https://mlsanity.com/paper/2607.11442/) (2026)

## Abstract (arXiv)

This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative models - autoencoders, autoregressive models, generative adversarial networks, normalizing flows, diffusion models, and flow matching - we demonstrate that they all fundamentally operate by transforming simple predefined distributions into complex target data distributions. This unifying perspective facilitates the transfer of methodological improvements between model architectures and provides a foundation for developing universal theoretical approaches, potentially leading to more efficient and effective generative modeling techniques.