# Understanding Diffusion Models: A Unified Perspective

arXiv: https://arxiv.org/abs/2208.11970 · HTML: https://mlsanity.com/paper/2208.11970/

## Key facts

- Cited by 340 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 27 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Deep Energy Estimator Networks](https://mlsanity.com/paper/1805.08306/) (2018)

## Built on by (most cited first, 30 of 340)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [DreamLLM: Synergistic Multimodal Comprehension and Creation](https://mlsanity.com/paper/2309.11499/) (2023)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [LLM-grounded Diffusion: Enhancing Prompt Understanding of Text-to-Image Diffusion Models with Large Language Models](https://mlsanity.com/paper/2305.13655/) (2023)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [Scaling Autoregressive Multi-Modal Models: Pretraining and Instruction Tuning](https://mlsanity.com/paper/2309.02591/) (2023)
- [StyleDiffusion: Controllable Disentangled Style Transfer via Diffusion Models](https://mlsanity.com/paper/2308.07863/) (2023)
- [Concept Sliders: LoRA Adaptors for Precise Control in Diffusion Models](https://mlsanity.com/paper/2311.12092/) (2023)
- [Fair Diffusion: Instructing Text-to-Image Generation Models on Fairness](https://mlsanity.com/paper/2302.10893/) (2023)
- [NeuralLift-360: Lifting An In-the-wild 2D Photo to A 3D Object with 360deg Views](https://mlsanity.com/paper/2211.16431/) (2022)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [AR-Diffusion: Auto-Regressive Diffusion Model for Text Generation](https://mlsanity.com/paper/2305.09515/) (2023)
- [GaussCtrl: Multi-View Consistent Text-Driven 3D Gaussian Splatting Editing](https://mlsanity.com/paper/2403.08733/) (2024)
- [Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervision](https://mlsanity.com/paper/2306.11719/) (2023)
- [HoloDiffusion: Training a 3D Diffusion Model using 2D Images](https://mlsanity.com/paper/2303.16509/) (2023)
- [Kosmos-G: Generating Images in Context with Multimodal Large Language Models](https://mlsanity.com/paper/2310.02992/) (2023)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (2024)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Controllable Generation with Text-to-Image Diffusion Models: A Survey](https://mlsanity.com/paper/2403.04279/) (2024)
- [BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Prediction](https://mlsanity.com/paper/2211.14304/) (2022)
- [Robustness of AI-Image Detectors: Fundamental Limits and Practical Attacks](https://mlsanity.com/paper/2310.00076/) (2023)
- [MM-Interleaved: Interleaved Image-Text Generative Modeling via Multi-modal Feature Synchronizer](https://mlsanity.com/paper/2401.10208/) (2024)
- [D4M: Dataset Distillation via Disentangled Diffusion Model](https://mlsanity.com/paper/2407.15138/) (2024)
- [Diffusion Action Segmentation](https://mlsanity.com/paper/2303.17959/) (2023)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)

## Abstract (arXiv)

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.