# One-Step Diffusion Distillation via Deep Equilibrium Models

arXiv: https://arxiv.org/abs/2401.08639 · HTML: https://mlsanity.com/paper/2401.08639/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 100 of its 115 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Placed in

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

## Builds on (most cited first, 30 of 100)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)

## Built on by (most cited first, 30 of 61)

- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [Diffusion Model-Based Image Editing: A Survey](https://mlsanity.com/paper/2402.17525/) (2024)
- [Consistency Models Made Easy](https://mlsanity.com/paper/2406.14548/) (2024)
- [DreamScene360: Unconstrained Text-to-3D Scene Generation with Panoramic Gaussian Splatting](https://mlsanity.com/paper/2404.06903/) (2024)
- [One-Step Diffusion Distillation through Score Implicit Matching](https://mlsanity.com/paper/2410.16794/) (2024)
- [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024)
- [Adversarial Score identity Distillation: Rapidly Surpassing the Teacher in One Step](https://mlsanity.com/paper/2410.14919/) (2024)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Reward Guided Latent Consistency Distillation](https://mlsanity.com/paper/2403.11027/) (2024)
- [Diff-Instruct++: Training One-step Text-to-image Generator Model to Align with Human Preferences](https://mlsanity.com/paper/2410.18881/) (2024)
- [Accelerating Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2402.09970/) (2024)
- [Flow Generator Matching](https://mlsanity.com/paper/2410.19310/) (2024)
- [Unleashing the Power of One-Step Diffusion based Image Super-Resolution via a Large-Scale Diffusion Discriminator](https://mlsanity.com/paper/2410.04224/) (2024)
- [Fixed Point Diffusion Models](https://mlsanity.com/paper/2401.08741/) (2024)
- [Ultra-Fast Language Generation via Discrete Diffusion Divergence Instruct](https://mlsanity.com/paper/2509.25035/) (2025)
- [REWIND: Real-Time Egocentric Whole-Body Motion Diffusion with Exemplar-Based Identity Conditioning](https://mlsanity.com/paper/2504.04956/) (2025)
- [ELT: Elastic Looped Transformers for Visual Generation](https://mlsanity.com/paper/2604.09168/) (2026)
- [Physics Informed Distillation for Diffusion Models](https://mlsanity.com/paper/2411.08378/) (2024)
- [AB-Cache: Training-Free Acceleration of Diffusion Models via Adams-Bashforth Cached Feature Reuse](https://mlsanity.com/paper/2504.10540/) (2025)
- [Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction](https://mlsanity.com/paper/2505.20755/) (2025)
- [Learning an Image Editing Model without Image Editing Pairs](https://mlsanity.com/paper/2510.14978/) (2025)
- [SoFlow: Solution Flow Models for One-Step Generative Modeling](https://mlsanity.com/paper/2512.15657/) (2025)
- [David and Goliath: Small One-step Model Beats Large Diffusion with Score Post-training](https://mlsanity.com/paper/2410.20898/) (2024)
- [One-Step Offline Distillation of Diffusion-based Models via Koopman Modeling](https://mlsanity.com/paper/2505.13358/) (2025)
- [Hierarchical VAE with a Diffusion-based VampPrior](https://mlsanity.com/paper/2412.01373/) (2024)
- [Modular MeanFlow: Towards Stable and Scalable One-Step Generative Modeling](https://mlsanity.com/paper/2508.17426/) (2025)
- [Learning Straight Flows: Variational Flow Matching for Efficient Generation](https://mlsanity.com/paper/2511.17583/) (2025)
- [Positive concave deep equilibrium models](https://mlsanity.com/paper/2402.04029/) (2024)
- [LeapAlign: Post-Training Flow Matching Models at Any Generation Step by Building Two-Step Trajectories](https://mlsanity.com/paper/2604.15311/) (2026)

## Abstract (arXiv)

Diffusion models excel at producing high-quality samples but naively require hundreds of iterations, prompting multiple attempts to distill the generation process into a faster network. However, many existing approaches suffer from a variety of challenges: the process for distillation training can be complex, often requiring multiple training stages, and the resulting models perform poorly when utilized in single-step generative applications. In this paper, we introduce a simple yet effective means of distilling diffusion models directly from initial noise to the resulting image. Of particular importance to our approach is to leverage a new Deep Equilibrium (DEQ) model as the distilled architecture: the Generative Equilibrium Transformer (GET). Our method enables fully offline training with just noise/image pairs from the diffusion model while achieving superior performance compared to existing one-step methods on comparable training budgets. We demonstrate that the DEQ architecture is crucial to this capability, as GET matches a 5× larger ViT in terms of FID scores while striking a critical balance of computational cost and image quality. Code, checkpoints, and datasets are available.