Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentation

Representing manipulation actions as 2D trajectories in the camera plane provides a compact and interpretable basis for learning complex 3D manipulation policies. However, it also creates challenges from out-of-frame trajectories and limited precision. We propose Pix2Act, an imitation learning method that addresses these challenges by generating continuous image-space keypoint trajectories in each camera plane and losslessly recovering end-effector poses via triangulation. This reformulates high-dimensional 3D control as a simpler, more learnable 2D prediction problem. Crucially, it aligns observations and actions in the same coordinate space, enabling equivariant transformations to jointly rotate individual camera images together with their image-space actions. We analyze the symmetry properties of this augmentation and design a network architecture that can fuse multiple camera views while respecting their per-view rotations. As a result, Pix2Act implicitly enlarges the support of the data distribution and learns invariant action structures across transformations, yielding improved generalization and overall performance. Across diverse simulated and real-world manipulation tasks, Pix2Act outperforms state-of-the-art baselines and remains robust under camera perturbations.

Action Map Policy: Learning 3D Closed-loop Manipulation via Pixel Classification

The action space poses a major challenge in robot learning, since it is often high-dimensional, can span long time horizons, and frequently admits multi-modal optimal solutions. A good choice of action representation and loss function can help to address these concerns, but there are often trade offs. We propose Action Map Policy (AMP), which casts 3D closed-loop manipulation policy learning as a classification problem in image space. While classification has been an effective formulation in generative language models, applying it to robot action learning is difficult because naively discretizing high-dimensional continuous actions explodes the token vocabulary. Our key idea is to project 3D actions onto the camera image planes and treat each pixel location as a discrete class, thus controlling dimensionality while retaining multi-modality. This method supports millimeter-level precision for high-dimensional actions without requiring a prohibitively large vocabulary, while preserving fine-grained pixel-wise visual signals. Furthermore, it can predict the entire action chunk in a single forward pass, avoiding complex noise scheduling and iterative denoising while achieving substantially faster inference than diffusion policies. Experiments on various manipulation tasks show that AMP outperforms strong baselines, achieving higher success rates, faster inference, and enhanced spatial reasoning.

When Life Gives You BC, Make Q-functions: Extracting Q-values from Behavior Cloning for On-Robot Reinforcement Learning

Behavior Cloning (BC) has emerged as a highly effective paradigm for robot learning. However, BC lacks a self-guided mechanism for online improvement after demonstrations have been collected. Existing offline-to-online learning methods often cause policies to replace previously learned good actions due to a distribution mismatch between offline data and online learning. In this work, we propose Q2RL, Q-Estimation and Q-Gating from BC for Reinforcement Learning, an algorithm for efficient offline-to-online learning. Our method consists of two parts: (1) Q-Estimation extracts a Q-function from a BC policy using a few interaction steps with the environment, followed by online RL with (2) Q-Gating, which switches between BC and RL policy actions based on their respective Q-values to collect samples for RL policy training. Across manipulation tasks from D4RL and robomimic benchmarks, Q2RL outperforms SOTA offline-to-online learning baselines on success rate and time to convergence. Q2RL is efficient enough to be applied in an on-robot RL setting, learning robust policies for contact-rich and high precision manipulation tasks such as pipe assembly and kitting, in 1-2 hours of online interaction, achieving success rates of up to 100% and up to 3.75x improvement against the original BC policy. Code and video are available at https://pages.rai-inst.com/q2rl_website/

You've Got a Golden Ticket: Improving Generative Robot Policies With A Single Noise Vector

What happens when a pretrained generative robot policy is provided a constant initial noise as input, rather than repeatedly sampling it from a Gaussian? We demonstrate that the performance of a pretrained, frozen diffusion or flow matching policy can be improved with respect to a downstream reward by swapping the sampling of initial noise from the prior distribution (typically isotropic Gaussian) with a well-chosen, constant initial noise input -- a golden ticket. We propose a search method to find golden tickets using Monte-Carlo policy evaluation that keeps the pretrained policy frozen, does not train any new networks, and is applicable to all diffusion/flow matching policies (and therefore many VLAs). Our approach to policy improvement makes no assumptions beyond being able to inject initial noise into the policy and calculate (sparse) task rewards of episode rollouts, making it deployable with no additional infrastructure or models. Our method improves the performance of policies in 38 out of 43 tasks across simulated and real-world robot manipulation benchmarks, with relative improvements in success rate by up to 58% for some simulated tasks, and 60% within 50 search episodes for real-world tasks. We also show unique benefits of golden tickets for multi-task settings: the diversity of behaviors from different tickets naturally defines a Pareto frontier for balancing different objectives (e.g., speed, success rates); in VLAs, we find that a golden ticket optimized for one task can also boost performance in other related tasks. We release a codebase with pretrained policies and golden tickets for simulation benchmarks using VLAs, diffusion policies, and flow matching policies.

Smoothness Errors in Dynamics Models and How to Avoid Them

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly similar to those of its neighbors. Unitary graph convolutions, which are mathematically constrained to preserve smoothness, have been proposed to address this issue. Despite this, in many physical systems, such as diffusion processes, smoothness naturally increases and unitarity may be overconstraining. In this paper, we systematically study the smoothing effects of different GNNs for dynamics modeling and prove that unitary convolutions hurt performance for such tasks. We propose relaxed unitary convolutions that balance smoothness preservation with the natural smoothing required for physical systems. We also generalize unitary and relaxed unitary convolutions from graphs to meshes. In experiments on PDEs such as the heat and wave equations over complex meshes and on weather forecasting, we find that our method outperforms several strong baselines, including mesh-aware transformers and equivariant neural networks.

DeepWeightFlow: Re-Basined Flow Matching for Generating Neural Network Weights

Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their symmetries. Several prior generative models are limited to generating partial neural network weights, particularly for larger models, such as ResNet and ViT. Those that do generate complete weights struggle with generation speed or require finetuning of the generated models. In this work, we present DeepWeightFlow, a Flow Matching model that operates directly in weight space to generate diverse and high-accuracy neural network weights for a variety of architectures, neural network sizes, and data modalities. The neural networks generated by DeepWeightFlow do not require fine-tuning to perform well and can scale to large networks. We apply Git Re-Basin and TransFusion for neural network canonicalization in the context of generative weight models to account for the impact of neural network permutation symmetries and to improve generation efficiency for larger model sizes. The generated networks excel at transfer learning, and ensembles of hundreds of neural networks can be generated in minutes, far exceeding the efficiency of diffusion-based methods. DeepWeightFlow models pave the way for more efficient and scalable generation of diverse sets of neural networks.

Discovering Lie Groups with Flow Matching

Symmetry is fundamental to understanding physical systems, and at the same time, can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data. To address this, we propose learning symmetries directly from data via flow matching on Lie groups. We formulate symmetry discovery as learning a distribution over a larger hypothesis group, such that the learned distribution matches the symmetries observed in data. Relative to previous works, our method, \lieflow, is more flexible in terms of the types of groups it can discover and requires fewer assumptions. Experiments on 2D and 3D point clouds demonstrate the successful discovery of discrete groups, including reflections by flow matching over the complex domain. We identify a key challenge where the symmetric arrangement of the target modes causes ``last-minute convergence,'' where samples remain stationary until relatively late in the flow, and introduce a novel interpolation scheme for flow matching for symmetry discovery.

On Uncertainty Calibration for Equivariant Functions

Data-sparse settings such as robotic manipulation, molecular physics, and galaxy morphology classification are some of the hardest domains for deep learning. For these problems, equivariant networks can help improve modeling across undersampled parts of the input space, and uncertainty estimation can guard against overconfidence. However, until now, the relationships between equivariance and model confidence, and more generally equivariance and model calibration, has yet to be studied. Since traditional classification and regression error terms show up in the definitions of calibration error, it is natural to suspect that previous work can be used to help understand the relationship between equivariance and calibration error. In this work, we present a theory relating equivariance to uncertainty estimation. By proving lower and upper bounds on uncertainty calibration errors (ECE and ENCE) under various equivariance conditions, we elucidate the generalization limits of equivariant models and illustrate how symmetry mismatch can result in miscalibration in both classification and regression. We complement our theoretical framework with numerical experiments that clarify the relationship between equivariance and uncertainty using a variety of real and simulated datasets, and we comment on trends with symmetry mismatch, group size, and aleatoric and epistemic uncertainties.

SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space

Diffusion Policies are effective at learning closed-loop manipulation policies from human demonstrations but generalize poorly to novel arrangements of objects in 3D space, hurting real-world performance. To address this issue, we propose Spherical Diffusion Policy (SDP), an SE(3) equivariant diffusion policy that adapts trajectories according to 3D transformations of the scene. Such equivariance is achieved by embedding the states, actions, and the denoising process in spherical Fourier space. Additionally, we employ novel spherical FiLM layers to condition the action denoising process equivariantly on the scene embeddings. Lastly, we propose a spherical denoising temporal U-net that achieves spatiotemporal equivariance with computational efficiency. In the end, SDP is end-to-end SE(3) equivariant, allowing robust generalization across transformed 3D scenes. SDP demonstrates a large performance improvement over strong baselines in 20 simulation tasks and 5 physical robot tasks including single-arm and bi-manual embodiments. Code is available at https://github.com/amazon-science/Spherical_Diffusion_Policy.

Symmetry in Neural Network Parameter Spaces

Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter space--transformations that leave the network function unchanged. These symmetries shape the loss landscape and constrain learning dynamics, offering a new lens for understanding optimization, generalization, and model complexity that complements existing theory of deep learning. This survey provides an overview of parameter space symmetry. We summarize existing literature, uncover connections between symmetry and learning theory, and identify gaps and opportunities in this emerging field.