# Learning dissection trajectories from expert surgical videos via imitation learning with equivariant diffusion

arXiv: https://arxiv.org/abs/2506.04716 · HTML: https://mlsanity.com/paper/2506.04716/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 36 of its 60 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)
- Offline RL and imitation learning from data / [Safe offline RL](https://mlsanity.com/offlinerl/safe-offline-rl/)

## Builds on (most cited first, 30 of 36)

- [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)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Exploring the Limitations of Behavior Cloning for Autonomous Driving](https://mlsanity.com/paper/1904.08980/) (2019)
- [Transporter Networks: Rearranging the Visual World for Robotic Manipulation](https://mlsanity.com/paper/2010.14406/) (2020)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Rendezvous: Attention Mechanisms for the Recognition of Surgical Action Triplets in Endoscopic Videos](https://mlsanity.com/paper/2109.03223/) (2021)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Surgical Data Science: Enabling Next-Generation Surgery](https://mlsanity.com/paper/1701.06482/) (2017)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Imitation Learning as f-Divergence Minimization](https://mlsanity.com/paper/1905.12888/) (2019)
- [Surgical Data Science -- from Concepts toward Clinical Translation](https://mlsanity.com/paper/2011.02284/) (2020)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Recursive Social Behavior Graph for Trajectory Prediction](https://mlsanity.com/paper/2004.10402/) (2020)
- [Strictly Batch Imitation Learning by Energy-based Distribution Matching](https://mlsanity.com/paper/2006.14154/) (2020)
- [The MAGICAL Benchmark for Robust Imitation](https://mlsanity.com/paper/2011.00401/) (2020)

## Built on by (most cited first, 2 of 2)

- [SurgiATM: A Physics-Guided Plug-and-Play Model for Deep Learning-Based Smoke Removal in Laparoscopic Surgery](https://mlsanity.com/paper/2511.05059/) (2025)
- [Multi-modal Representation Fusion for Long-term Microsurgical Anastomosis Trajectory Anticipation](https://mlsanity.com/paper/2610.14492/) (2026)

## Abstract (arXiv)

Endoscopic Submucosal Dissection (ESD) is a well-established technique for removing epithelial lesions. Predicting dissection trajectories in ESD videos offers significant potential for enhancing surgical skill training and simplifying the learning process, yet this area remains underexplored. While imitation learning has shown promise in acquiring skills from expert demonstrations, challenges persist in handling uncertain future movements, learning geometric symmetries, and generalizing to diverse surgical scenarios. To address these, we introduce a novel approach: Implicit Diffusion Policy with Equivariant Representations for Imitation Learning (iDPOE). Our method models expert behavior through a joint state action distribution, capturing the stochastic nature of dissection trajectories and enabling robust visual representation learning across various endoscopic views. By incorporating a diffusion model into policy learning, iDPOE ensures efficient training and sampling, leading to more accurate predictions and better generalization. Additionally, we enhance the model's ability to generalize to geometric symmetries by embedding equivariance into the learning process. To address state mismatches, we develop a forward-process guided action inference strategy for conditional sampling. Using an ESD video dataset of nearly 2000 clips, experimental results show that our approach surpasses state-of-the-art methods, both explicit and implicit, in trajectory prediction. To the best of our knowledge, this is the first application of imitation learning to surgical skill development for dissection trajectory prediction.