# Accelerating Image Generation with Sub-path Linear Approximation Model

arXiv: https://arxiv.org/abs/2404.13903 · HTML: https://mlsanity.com/paper/2404.13903/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 50 of its 55 references that are in the map.
- First posted on arXiv 22 Apr 2024.

## Placed in

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

## Builds on (most cited first, 30 of 50)

- [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)
- [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)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [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)
- [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)
- [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)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [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)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)

## Built on by (most cited first, 14 of 14)

- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Accelerating Auto-regressive Text-to-Image Generation with Training-free Speculative Jacobi Decoding](https://mlsanity.com/paper/2410.01699/) (2024)
- [Adversarial Diffusion Compression for Real-World Image Super-Resolution](https://mlsanity.com/paper/2411.13383/) (2024)
- [Diffusion Model-Based Video Editing: A Survey](https://mlsanity.com/paper/2407.07111/) (2024)
- [AWT: Transferring Vision-Language Models via Augmentation, Weighting, and Transportation](https://mlsanity.com/paper/2407.04603/) (2024)
- [Unleashing Vecset Diffusion Model for Fast Shape Generation](https://mlsanity.com/paper/2503.16302/) (2025)
- [NitroFusion: High-Fidelity Single-Step Diffusion through Dynamic Adversarial Training](https://mlsanity.com/paper/2412.02030/) (2024)
- [TimeStep Master: Asymmetrical Mixture of Timestep LoRA Experts for Versatile and Efficient Diffusion Models in Vision](https://mlsanity.com/paper/2503.07416/) (2025)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [Differentiable Solver Search for Fast Diffusion Sampling](https://mlsanity.com/paper/2505.21114/) (2025)
- [ProReflow: Progressive Reflow with Decomposed Velocity](https://mlsanity.com/paper/2503.04824/) (2025)
- [DMM: Building a Versatile Image Generation Model via Distillation-Based Model Merging](https://mlsanity.com/paper/2504.12364/) (2025)
- [SJD++: Improved Speculative Jacobi Decoding for Training-free Acceleration of Discrete Auto-regressive Text-to-Image Generation](https://mlsanity.com/paper/2512.07503/) (2025)
- [TurboClear: One-Step Object-Effect Removal via Region-Calibrated Distribution Matching and Fusion](https://mlsanity.com/paper/2608.01288/) (2026)

## Abstract (arXiv)

Diffusion models have significantly advanced the state of the art in image, audio, and video generation tasks. However, their applications in practical scenarios are hindered by slow inference speed. Drawing inspiration from the approximation strategies utilized in consistency models, we propose the Sub-path Linear Approximation Model (SLAM), which accelerates diffusion models while maintaining high-quality image generation. SLAM treats the PF-ODE trajectory as a series of PF-ODE sub-paths divided by sampled points, and harnesses sub-path linear (SL) ODEs to form a progressive and continuous error estimation along each individual PF-ODE sub-path. The optimization on such SL-ODEs allows SLAM to construct denoising mappings with smaller cumulative approximated errors. An efficient distillation method is also developed to facilitate the incorporation of more advanced diffusion models, such as latent diffusion models. Our extensive experimental results demonstrate that SLAM achieves an efficient training regimen, requiring only 6 A100 GPU days to produce a high-quality generative model capable of 2 to 4-step generation with high performance. Comprehensive evaluations on LAION, MS COCO 2014, and MS COCO 2017 datasets also illustrate that SLAM surpasses existing acceleration methods in few-step generation tasks, achieving state-of-the-art performance both on FID and the quality of the generated images.