# Catch-Up Distillation: You Only Need to Train Once for Accelerating Sampling

arXiv: https://arxiv.org/abs/2305.10769 · HTML: https://mlsanity.com/paper/2305.10769/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 48 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [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)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)

## Built on by (most cited first, 13 of 13)

- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Robust Classification via a Single Diffusion Model](https://mlsanity.com/paper/2305.15241/) (2023)
- [CAT-DM: Controllable Accelerated Virtual Try-on with Diffusion Model](https://mlsanity.com/paper/2311.18405/) (2023)
- [Your Diffusion Model is Secretly a Certifiably Robust Classifier](https://mlsanity.com/paper/2402.02316/) (2024)
- [EMQ: Evolving Training-free Proxies for Automated Mixed Precision Quantization](https://mlsanity.com/paper/2307.10554/) (2023)
- [Rethinking Centered Kernel Alignment in Knowledge Distillation](https://mlsanity.com/paper/2401.11824/) (2024)
- [IV-Mixed Sampler: Leveraging Image Diffusion Models for Enhanced Video Synthesis](https://mlsanity.com/paper/2410.04171/) (2024)
- [Bag of Design Choices for Inference of High-Resolution Masked Generative Transformer](https://mlsanity.com/paper/2411.10781/) (2024)
- [Efficient Generative Model Training via Embedded Representation Warmup](https://mlsanity.com/paper/2504.10188/) (2025)
- [LIVEditor-14B: Lightning Unified Video Editing via In-Context Sparse Attention](https://mlsanity.com/paper/2605.04569/) (2026)
- [TVT: Training-Free Vision Transformer Search on Tiny Datasets](https://mlsanity.com/paper/2311.14337/) (2023)
- [CoRe^2: Collect, Reflect and Refine to Generate Better and Faster](https://mlsanity.com/paper/2503.09662/) (2025)
- [Learning Quantized Adaptive Conditions for Diffusion Models](https://mlsanity.com/paper/2409.17487/) (2024)

## Abstract (arXiv)

Diffusion Probability Models (DPMs) have made impressive advancements in various machine learning domains. However, achieving high-quality synthetic samples typically involves performing a large number of sampling steps, which impedes the possibility of real-time sample synthesis. Traditional accelerated sampling algorithms via knowledge distillation rely on pre-trained model weights and discrete time step scenarios, necessitating additional training sessions to achieve their goals. To address these issues, we propose the Catch-Up Distillation (CUD), which encourages the current moment output of the velocity estimation model ``catch up'' with its previous moment output. Specifically, CUD adjusts the original Ordinary Differential Equation (ODE) training objective to align the current moment output with both the ground truth label and the previous moment output, utilizing Runge-Kutta-based multi-step alignment distillation for precise ODE estimation while preventing asynchronous updates. Furthermore, we investigate the design space for CUDs under continuous time-step scenarios and analyze how to determine the suitable strategies. To demonstrate CUD's effectiveness, we conduct thorough ablation and comparison experiments on CIFAR-10, MNIST, and ImageNet-64. On CIFAR-10, we obtain a FID of 2.80 by sampling in 15 steps under one-session training and the new state-of-the-art FID of 3.37 by sampling in one step with additional training. This latter result necessitated only 620k iterations with a batch size of 128, in contrast to Consistency Distillation, which demanded 2100k iterations with a larger batch size of 256. Our code is released at https://anonymous.4open.science/r/Catch-Up-Distillation-E31F.