# Pruning for Sparse Diffusion Models based on Gradient Flow

arXiv: https://arxiv.org/abs/2501.09464 · HTML: https://mlsanity.com/paper/2501.09464/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 16 Jan 2025.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Structural Pruning for Diffusion Models](https://mlsanity.com/paper/2305.10924/) (2023)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [Content-based Unrestricted Adversarial Attack](https://mlsanity.com/paper/2305.10665/) (2023)
- [Only Train Once: A One-Shot Neural Network Training And Pruning Framework](https://mlsanity.com/paper/2107.07467/) (2021)
- [A Gradient Flow Framework For Analyzing Network Pruning](https://mlsanity.com/paper/2009.11839/) (2020)
- [SparseDM: Toward Sparse Efficient Diffusion Models](https://mlsanity.com/paper/2404.10445/) (2024)
- [Soft Masking for Cost-Constrained Channel Pruning](https://mlsanity.com/paper/2211.02206/) (2022)
- [Training Recipe for N:M Structured Sparsity with Decaying Pruning Mask](https://mlsanity.com/paper/2209.07617/) (2022)

## Built on by (most cited first, 5 of 5)

- [TS-DP: Reinforcement Speculative Decoding For Temporal Adaptive Diffusion Policy Acceleration](https://mlsanity.com/paper/2512.15773/) (2025)
- [Phase-Aligned RoPE for Mixed-Resolution Diffusion Transformer](https://mlsanity.com/paper/2511.19778/) (2025)
- [DiTReducio: A Training-Free Acceleration for DiT-Based TTS via Progressive Calibration](https://mlsanity.com/paper/2509.09748/) (2025)
- [LowDiff: Efficient Diffusion Sampling with Low-Resolution Condition](https://mlsanity.com/paper/2509.15342/) (2025)
- [NanoFLUX: Distillation-Driven Compression of Large Text-to-Image Generation Models for Mobile Devices](https://mlsanity.com/paper/2602.06879/) (2026)

## Abstract (arXiv)

Diffusion Models (DMs) have impressive capabilities among generation models, but are limited to slower inference speeds and higher computational costs. Previous works utilize one-shot structure pruning to derive lightweight DMs from pre-trained ones, but this approach often leads to a significant drop in generation quality and may result in the removal of crucial weights. Thus we propose a iterative pruning method based on gradient flow, including the gradient flow pruning process and the gradient flow pruning criterion. We employ a progressive soft pruning strategy to maintain the continuity of the mask matrix and guide it along the gradient flow of the energy function based on the pruning criterion in sparse space, thereby avoiding the sudden information loss typically caused by one-shot pruning. Gradient-flow based criterion prune parameters whose removal increases the gradient norm of loss function and can enable fast convergence for a pruned model in iterative pruning stage. Our extensive experiments on widely used datasets demonstrate that our method achieves superior performance in efficiency and consistency with pre-trained models.