# Optimizing for the Shortest Path in Denoising Diffusion Model

arXiv: https://arxiv.org/abs/2503.03265 · HTML: https://mlsanity.com/paper/2503.03265/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 37 references that are in the map.
- First posted on arXiv 5 Mar 2025.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (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)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Label-Efficient Semantic Segmentation with Diffusion Models](https://mlsanity.com/paper/2112.03126/) (2021)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)
- [gDDIM: Generalized denoising diffusion implicit models](https://mlsanity.com/paper/2206.05564/) (2022)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [BOOT: Data-free Distillation of Denoising Diffusion Models with Bootstrapping](https://mlsanity.com/paper/2306.05544/) (2023)
- [Fast ODE-based Sampling for Diffusion Models in Around 5 Steps](https://mlsanity.com/paper/2312.00094/) (2023)
- [Residual Denoising Diffusion Models](https://mlsanity.com/paper/2308.13712/) (2023)
- [Spiking Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.17046/) (2023)
- [Resfusion: Denoising Diffusion Probabilistic Models for Image Restoration Based on Prior Residual Noise](https://mlsanity.com/paper/2311.14900/) (2023)
- [Distilling ODE Solvers of Diffusion Models into Smaller Steps](https://mlsanity.com/paper/2309.16421/) (2023)

## Built on by (most cited first, 6 of 6)

- [LeMiCa: Lexicographic Minimax Path Caching for Efficient Diffusion-Based Video Generation](https://mlsanity.com/paper/2511.00090/) (2025)
- [MeanCache: From Instantaneous to Average Velocity for Accelerating Flow Matching Inference](https://mlsanity.com/paper/2601.19961/) (2026)
- [Chain-of-Trajectories: Unlocking the Intrinsic Generative Optimality of Diffusion Models via Graph-Theoretic Planning](https://mlsanity.com/paper/2603.14704/) (2026)
- [OTCache: Optimal Transport for Geometry-Aware Caching in Diffusion Models](https://mlsanity.com/paper/2606.31026/) (2026)
- [SSPFormer: Self-Supervised Pretrained Transformer for MRI Images](https://mlsanity.com/paper/2601.12747/) (2026)
- [Beyond Geometry: Artistic Disparity Synthesis for Immersive 2D-to-3D](https://mlsanity.com/paper/2603.05906/) (2026)

## Abstract (arXiv)

In this research, we propose a novel denoising diffusion model based on shortest-path modeling that optimizes residual propagation to enhance both denoising efficiency and quality. Drawing on Denoising Diffusion Implicit Models (DDIM) and insights from graph theory, our model, termed the Shortest Path Diffusion Model (ShortDF), treats the denoising process as a shortest-path problem aimed at minimizing reconstruction error. By optimizing the initial residuals, we improve the efficiency of the reverse diffusion process and the quality of the generated samples. Extensive experiments on multiple standard benchmarks demonstrate that ShortDF significantly reduces diffusion time (or steps) while enhancing the visual fidelity of generated samples compared to prior arts. This work, we suppose, paves the way for interactive diffusion-based applications and establishes a foundation for rapid data generation. Code is available at https://github.com/UnicomAI/ShortDF.