# EM Distillation for One-step Diffusion Models

arXiv: https://arxiv.org/abs/2405.16852 · HTML: https://mlsanity.com/paper/2405.16852/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 66 of its 77 references that are in the map.
- First posted on arXiv 27 May 2024.

## Placed in

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

## Builds on (most cited first, 30 of 66)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)

## Built on by (most cited first, 30 of 62)

- [From Slow Bidirectional to Fast Autoregressive Video Diffusion Models](https://mlsanity.com/paper/2412.07772/) (2024)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillation](https://mlsanity.com/paper/2503.09641/) (2025)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [One-step Diffusion Models with f-Divergence Distribution Matching](https://mlsanity.com/paper/2502.15681/) (2025)
- [Diffusion Model Predictive Control](https://mlsanity.com/paper/2410.05364/) (2024)
- [FlashWorld: High-quality 3D Scene Generation within Seconds](https://mlsanity.com/paper/2510.13678/) (2025)
- [Diff-Instruct++: Training One-step Text-to-image Generator Model to Align with Human Preferences](https://mlsanity.com/paper/2410.18881/) (2024)
- [DOLLAR: Few-Step Video Generation via Distillation and Latent Reward Optimization](https://mlsanity.com/paper/2412.15689/) (2024)
- [DKDM: Data-Free Knowledge Distillation for Diffusion Models with Any Architecture](https://mlsanity.com/paper/2409.03550/) (2024)
- [Truncated Consistency Models](https://mlsanity.com/paper/2410.14895/) (2024)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [BridgeDrive: Diffusion Bridge Policy for Closed-Loop Trajectory Planning in Autonomous Driving](https://mlsanity.com/paper/2509.23589/) (2025)
- [Ultra-Fast Language Generation via Discrete Diffusion Divergence Instruct](https://mlsanity.com/paper/2509.25035/) (2025)
- [Variational Distillation of Diffusion Policies into Mixture of Experts](https://mlsanity.com/paper/2406.12538/) (2024)
- [VCT: Training Consistency Models with Variational Noise Coupling](https://mlsanity.com/paper/2502.18197/) (2025)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching](https://mlsanity.com/paper/2406.10808/) (2024)
- [Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction](https://mlsanity.com/paper/2505.20755/) (2025)
- [RayFlow: Instance-Aware Diffusion Acceleration via Adaptive Flow Trajectories](https://mlsanity.com/paper/2503.07699/) (2025)
- [Multi-student Diffusion Distillation for Better One-step Generators](https://mlsanity.com/paper/2410.23274/) (2024)
- [Learning to Integrate Diffusion ODEs by Averaging the Derivatives](https://mlsanity.com/paper/2505.14502/) (2025)
- [David and Goliath: Small One-step Model Beats Large Diffusion with Score Post-training](https://mlsanity.com/paper/2410.20898/) (2024)
- [DiffRatio: Training One-Step Diffusion Models Without Teacher Supervision](https://mlsanity.com/paper/2502.08005/) (2025)
- [Autoregressive Distillation of Diffusion Transformers](https://mlsanity.com/paper/2504.11295/) (2025)
- [Modular MeanFlow: Towards Stable and Scalable One-Step Generative Modeling](https://mlsanity.com/paper/2508.17426/) (2025)
- [Learnable Sampler Distillation for Discrete Diffusion Models](https://mlsanity.com/paper/2509.19962/) (2025)
- [IDLM: Inverse-distilled Diffusion Language Models](https://mlsanity.com/paper/2602.19066/) (2026)
- [SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories](https://mlsanity.com/paper/2502.16972/) (2025)

## Abstract (arXiv)

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.