# Geometry Guided Self-Consistency for Physical AI

arXiv: https://arxiv.org/abs/2605.08638 · HTML: https://mlsanity.com/paper/2605.08638/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 26 references that are in the map.
- First posted on arXiv 9 May 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics](https://mlsanity.com/paper/2506.01844/) (2025)
- [RoboTwin 2.0: A Scalable Data Generator and Benchmark with Strong Domain Randomization for Robust Bimanual Robotic Manipulation](https://mlsanity.com/paper/2506.18088/) (2025)
- [Evaluating Real-World Robot Manipulation Policies in Simulation](https://mlsanity.com/paper/2405.05941/) (2024)
- [World Action Models are Zero-shot Policies](https://mlsanity.com/paper/2602.15922/) (2026)
- [Fast-WAM: Do World Action Models Need Test-time Future Imagination?](https://mlsanity.com/paper/2603.16666/) (2026)
- [X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Model](https://mlsanity.com/paper/2510.10274/) (2025)
- [Cosmos Policy: Fine-Tuning Video Models for Visuomotor Control and Planning](https://mlsanity.com/paper/2601.16163/) (2026)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [StarVLA: A Lego-like Codebase for Vision-Language-Action Model Developing](https://mlsanity.com/paper/2604.05014/) (2026)
- [Steering Your Generalists: Improving Robotic Foundation Models via Value Guidance](https://mlsanity.com/paper/2410.13816/) (2024)
- [LeRobot: An Open-Source Library for End-to-End Robot Learning](https://mlsanity.com/paper/2602.22818/) (2026)
- [RoboMonkey: Scaling Test-Time Sampling and Verification for Vision-Language-Action Models](https://mlsanity.com/paper/2506.17811/) (2025)
- [Verifier-free Test-Time Sampling for Vision-Language-Action Models](https://mlsanity.com/paper/2510.05681/) (2025)
- [Steering Vision-Language-Action Models as Anti-Exploration: A Test-Time Scaling Approach](https://mlsanity.com/paper/2512.02834/) (2025)
- [vla-eval: A Unified Evaluation Harness for Vision-Language-Action Models](https://mlsanity.com/paper/2603.13966/) (2026)
- [KDPE: A Kernel Density Estimation Strategy for Diffusion Policy Trajectory Selection](https://mlsanity.com/paper/2508.10511/) (2025)

## Built on by (most cited first, 1 of 1)

- [IMPLY: Physically Anchored Consistency for World-Model Rollouts](https://mlsanity.com/paper/2609.12441/) (2026)

## Abstract (arXiv)

State-of-the-art physical AI models generate a chunk of actions per inference through diffusion or flow matching, iteratively refining an initial noise sample into an action trajectory. Because this inference process is inherently stochastic, committing to a single trajectory per round is brittle, and this brittleness compounds across the many sequential rounds that comprise a complete episode. We introduce KeyStone, an inference-time self-consistency method for diffusion-based action generation that draws K candidate action chunks in parallel from a shared model context, clusters them in continuous action space, and returns the medoid of the largest cluster -- no additional model required. Two properties make this practical. First, the compact nature of action trajectories makes diffusion inference memory-bandwidth bound, leaving spare compute capacity to run K chains in parallel with no additional wall-clock latency. Second, unlike token or pixel spaces where distance carries no semantic meaning and selection requires a learned judge, action chunks are geometrically structured such that Euclidean distance directly reflects physical similarity, making selection principled and judge-free. Across diverse vision-language-action models (VLAs) and world-action models (WAMs), KeyStone improves task success rates by up to 13.3% over single-trajectory sampling with negligible latency overhead, while having on par accuracy with model-based selectors at no training cost. We open source KeyStone at https://github.com/dywsjtu/keystone.