# Diffusion Trajectory Modeling for Semantic Correspondence

arXiv: https://arxiv.org/abs/2609.15357 · HTML: https://mlsanity.com/paper/2609.15357/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 26 of its 31 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [Deep ViT Features as Dense Visual Descriptors](https://mlsanity.com/paper/2112.05814/) (2021)
- [A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence](https://mlsanity.com/paper/2305.15347/) (2023)
- [Diffusion Hyperfeatures: Searching Through Time and Space for Semantic Correspondence](https://mlsanity.com/paper/2305.14334/) (2023)
- [SPair-71k: A Large-scale Benchmark for Semantic Correspondence](https://mlsanity.com/paper/1908.10543/) (2019)
- [AP-10K: A Benchmark for Animal Pose Estimation in the Wild](https://mlsanity.com/paper/2108.12617/) (2021)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Telling Left from Right: Identifying Geometry-Aware Semantic Correspondence](https://mlsanity.com/paper/2311.17034/) (2023)
- [CATs: Cost Aggregation Transformers for Visual Correspondence](https://mlsanity.com/paper/2106.02520/) (2021)
- [CATs++: Boosting Cost Aggregation with Convolutions and Transformers](https://mlsanity.com/paper/2202.06817/) (2022)
- [SD4Match: Learning to Prompt Stable Diffusion Model for Semantic Matching](https://mlsanity.com/paper/2310.17569/) (2023)
- [Unleashing Diffusion Transformers for Visual Correspondence by Modulating Massive Activations](https://mlsanity.com/paper/2505.18584/) (2025)

## Abstract (arXiv)

Diffusion models generate images through an iterative diffusion process, and recent studies have demonstrated that the intermediate feature maps produced during this process contain rich visual representations, leading to their adoption across a variety of downstream tasks. However, most existing approaches are limited to either using a single feature map at a specific timestep or aggregating feature maps across multiple timesteps. We observe that intermediate representations in the diffusion process form meaningful trajectories along the time axis. In particular, the representation of each spatial patch evolves progressively throughout the generative process, encoding semantics that are difficult to capture from static snapshots alone. This observation motivates the need to treat diffusion representations as temporally structured trajectories rather than static snapshots. To this end, we propose Diffusion Trajectory Modeling (DTM), a framework that interprets the temporal evolution of each spatial patch as a trajectory and leverages it for semantic correspondence. By effectively modeling patch-wise trajectories generated across multiple timesteps, DTM captures correspondence cues that prior methods are not designed to capture. We further demonstrate empirically that spatially corresponding patches form similar trajectory patterns throughout the diffusion process, suggesting that the temporal axis of diffusion carries semantic information. Experiments on SPair-71k, SPair-U and AP-10K show that DTM achieves strong performance, presenting a new perspective for exploiting diffusion representations from a trajectory-centric viewpoint.