# Phase-Conditioned Affordance Fields for SE(3)-Equivariant Visuomotor Policies

arXiv: https://arxiv.org/abs/2610.17281 · HTML: https://mlsanity.com/paper/2610.17281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 37 references that are in the map.
- First posted on arXiv 12 Oct 2026.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [robosuite: A Modular Simulation Framework and Benchmark for Robot Learning](https://mlsanity.com/paper/2009.12293/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Act3D: 3D Feature Field Transformers for Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2306.17817/) (2023)
- [VAT-Mart: Learning Visual Action Trajectory Proposals for Manipulating 3D ARTiculated Objects](https://mlsanity.com/paper/2106.14440/) (2021)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Robo-ABC: Affordance Generalization Beyond Categories via Semantic Correspondence for Robot Manipulation](https://mlsanity.com/paper/2401.07487/) (2024)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [AdaAfford: Learning to Adapt Manipulation Affordance for 3D Articulated Objects via Few-shot Interactions](https://mlsanity.com/paper/2112.00246/) (2021)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Sample Efficient Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2202.09468/) (2022)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [Generalizable Humanoid Manipulation with 3D Diffusion Policies](https://mlsanity.com/paper/2410.10803/) (2024)
- [Equivariant Transporter Network](https://mlsanity.com/paper/2202.09400/) (2022)
- [RT-Affordance: Affordances are Versatile Intermediate Representations for Robot Manipulation](https://mlsanity.com/paper/2411.02704/) (2024)
- [AffordDP: Generalizable Diffusion Policy with Transferable Affordance](https://mlsanity.com/paper/2412.03142/) (2024)

## Abstract (arXiv)

SE(3)-equivariance provides a useful geometric inductive bias for visuomotor policies, encoding that actions covary with rigid transformations of the observation. However, existing SE(3)-equivariant visuomotor policies build this bias on a global equivariance assumption that treats the entire observation as governed by a single rigid transformation, which breaks down in real-world manipulation tasks where the task-relevant region changes across different objects. We address this by learning a phase-conditioned affordance field (PAF) over the observed point cloud, a per-point score that the SE(3)-equivariant policy uses in two complementary ways. Its score-weighted centroid serves as a learned, phase-conditioned anchor that canonicalizes the observation and the action around the active region, replacing the fixed gripper-frame reference, and the score itself is appended as a per-point feature. This introduces a local geometric inductive bias, while preserving the policy's global SE(3) equivariance. We validate on multiple MimicGen tasks under varying spatial randomization, and PAF consistently improves the success rate of the underlying policy. On multi-object real-robot tasks, PAF outperforms baselines and keeps its lead under lighting variations.