# A Complete Recipe for Diffusion Generative Models

arXiv: https://arxiv.org/abs/2303.01748 · HTML: https://mlsanity.com/paper/2303.01748/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 54 of its 72 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Placed in

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

## Builds on (most cited first, 30 of 54)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [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)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [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)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)

## Built on by (most cited first, 17 of 17)

- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Variational Control for Guidance in Diffusion Models](https://mlsanity.com/paper/2502.03686/) (2025)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groups](https://mlsanity.com/paper/2405.16381/) (2024)
- [Fast Samplers for Inverse Problems in Iterative Refinement Models](https://mlsanity.com/paper/2405.17673/) (2024)
- [Diffusion Rejection Sampling](https://mlsanity.com/paper/2405.17880/) (2024)
- [Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models](https://mlsanity.com/paper/2411.18702/) (2024)
- [The Missing U for Efficient Diffusion Models](https://mlsanity.com/paper/2310.20092/) (2023)
- [Data Can Speak for Itself: Quality-guided Utilization of Wireless Synthetic Data](https://mlsanity.com/paper/2506.23174/) (2025)
- [Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance](https://mlsanity.com/paper/2602.15914/) (2026)
- [Sparse Data Diffusion for Scientific Simulations in Biology and Physics](https://mlsanity.com/paper/2502.02448/) (2025)
- [Control-Augmented Autoregressive Diffusion for Data Assimilation](https://mlsanity.com/paper/2510.06637/) (2025)
- [Flow Map Learning via Nongradient Vector Flow](https://mlsanity.com/paper/2607.26398/) (2026)
- [Towards Fast Stochastic Sampling in Diffusion Generative Models](https://mlsanity.com/paper/2402.07211/) (2024)
- [Dataset Color Quantization: A Training-Oriented Framework for Dataset-Level Compression](https://mlsanity.com/paper/2602.20650/) (2026)
- [Variational Test-time Optimization for Diffusion Synchronization](https://mlsanity.com/paper/2606.15614/) (2026)

## Abstract (arXiv)

Score-based Generative Models (SGMs) have demonstrated exceptional synthesis outcomes across various tasks. However, the current design landscape of the forward diffusion process remains largely untapped and often relies on physical heuristics or simplifying assumptions. Utilizing insights from the development of scalable Bayesian posterior samplers, we present a complete recipe for formulating forward processes in SGMs, ensuring convergence to the desired target distribution. Our approach reveals that several existing SGMs can be seen as specific manifestations of our framework. Building upon this method, we introduce Phase Space Langevin Diffusion (PSLD), which relies on score-based modeling within an augmented space enriched by auxiliary variables akin to physical phase space. Empirical results exhibit the superior sample quality and improved speed-quality trade-off of PSLD compared to various competing approaches on established image synthesis benchmarks. Remarkably, PSLD achieves sample quality akin to state-of-the-art SGMs (FID: 2.10 for unconditional CIFAR-10 generation). Lastly, we demonstrate the applicability of PSLD in conditional synthesis using pre-trained score networks, offering an appealing alternative as an SGM backbone for future advancements. Code and model checkpoints can be accessed at urlhttps://github.com/mandt-lab/PSLD.