# TopoCut: Learning Multi-Step Cutting with Spectral Rewards and Discrete Diffusion Policies

arXiv: https://arxiv.org/abs/2509.19712 · HTML: https://mlsanity.com/paper/2509.19712/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 22 of 22)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Sim-to-Real Reinforcement Learning for Deformable Object Manipulation](https://mlsanity.com/paper/1806.07851/) (2018)
- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [FlingBot: The Unreasonable Effectiveness of Dynamic Manipulation for Cloth Unfolding](https://mlsanity.com/paper/2105.03655/) (2021)
- [Interactive Perception: Leveraging Action in Perception and Perception in Action](https://mlsanity.com/paper/1604.03670/) (2016)
- [RoboCraft: Learning to See, Simulate, and Shape Elasto-Plastic Objects with Graph Networks](https://mlsanity.com/paper/2205.02909/) (2022)
- [DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting](https://mlsanity.com/paper/2105.12244/) (2021)
- [Learning Multi-Object Dynamics with Compositional Neural Radiance Fields](https://mlsanity.com/paper/2202.11855/) (2022)
- [ToolFlowNet: Robotic Manipulation with Tools via Predicting Tool Flow from Point Clouds](https://mlsanity.com/paper/2211.09006/) (2022)
- [Act the Part: Learning Interaction Strategies for Articulated Object Part Discovery](https://mlsanity.com/paper/2105.01047/) (2021)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation](https://mlsanity.com/paper/2303.02346/) (2023)
- [Iterative Residual Policy: for Goal-Conditioned Dynamic Manipulation of Deformable Objects](https://mlsanity.com/paper/2203.00663/) (2022)
- [Improvisation through Physical Understanding: Using Novel Objects as Tools with Visual Foresight](https://mlsanity.com/paper/1904.05538/) (2019)
- [Long-Horizon Multi-Robot Rearrangement Planning for Construction Assembly](https://mlsanity.com/paper/2106.02489/) (2021)
- [RoboNinja: Learning an Adaptive Cutting Policy for Multi-Material Objects](https://mlsanity.com/paper/2302.11553/) (2023)
- [Sim2real Transfer Learning for Point Cloud Segmentation: An Industrial Application Case on Autonomous Disassembly](https://mlsanity.com/paper/2301.05033/) (2023)
- [Contact Points Discovery for Soft-Body Manipulations with Differentiable Physics](https://mlsanity.com/paper/2205.02835/) (2022)
- [TANDEM: Learning Joint Exploration and Decision Making with Tactile Sensors](https://mlsanity.com/paper/2203.00798/) (2022)
- [TANDEM3D: Active Tactile Exploration for 3D Object Recognition](https://mlsanity.com/paper/2209.08772/) (2022)
- [Planning with Spatial-Temporal Abstraction from Point Clouds for Deformable Object Manipulation](https://mlsanity.com/paper/2210.15751/) (2022)

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

- [CulinaryCut-VLAP: A Vision-Language-Action-Physics Framework for Food Cutting via a Force-Aware Material Point Method](https://mlsanity.com/paper/2601.06451/) (2026)
- [A Hierarchical Approach to Imitation Learning for Manipulation Tasks Requiring Time Varying Forces](https://mlsanity.com/paper/2608.03103/) (2026)

## Abstract (arXiv)

Robotic manipulation tasks involving cutting deformable objects remain challenging due to complex topological behaviors, difficulties in perceiving dense object states, and the lack of efficient evaluation methods for cutting outcomes. In this paper, we introduce TopoCut, a comprehensive benchmark for multi-step robotic cutting tasks that integrates a cutting environment and generalized policy learning. TopoCut is built upon three core components: (1) We introduce a high-fidelity simulation environment based on a particle-based elastoplastic solver with compliant von Mises constitutive models, augmented by a novel damage-driven topology discovery mechanism that enables accurate tracking of multiple cutting pieces. (2) We develop a comprehensive reward design that integrates the topology discovery with a pose-invariant spectral reward model based on Laplace-Beltrami eigenanalysis, facilitating consistent and robust assessment of cutting quality. (3) We propose an integrated policy learning pipeline, where a dynamics-informed perception module predicts topological evolution and produces particle-wise, topology-aware embeddings to support PDDP (Particle-based Score-Entropy Discrete Diffusion Policy) for goal-conditioned policy learning. Extensive experiments demonstrate that TopoCut supports trajectory generation, scalable learning, precise evaluation, and strong generalization across diverse object geometries, scales, poses, and cutting goals.