拡散モデルの内在的幾何学を制約付き逆運動学で探る
Exploring the Intrinsic Geometry of Diffusion Models with Constrained Inverse Kinematics
拡散モデルがデータ多様体の幾何構造を学習できるかを、解析的に幾何が分かる制約付き逆運動学タスクで検証した論文。
詳しい要約
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2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
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著者: Miguel Angel Rogel Garcia, Phone Thiha Kyaw, Jonathan Kelly
分類: cs.RO
原文アブストラクト
Recent studies suggest that diffusion models can recover geometric structure in the data manifolds they are trained on, yet the supporting evidence has so far come mostly from natural-image data, where the underlying geometry itself is unknown. We study this question in a setting where the geometry is analytically tractable: constrained inverse kinematics (IK). Each task-space constraint defines a configuration-space manifold with known intrinsic dimension, giving direct ground truth for evaluating the geometry learned by the model. For each of the 6-DoF UR5 and 7-DoF Franka, we train a single conditional diffusion model across seven constraint families, spanning solution manifolds from discrete IK branches to self-motion manifolds. Our empirical results reveal that the intrinsic dimension recovered from the model's score function matches the analytical degrees of freedom of the corresponding constraint manifold across both robots. Moreover, linear interpolation in the latent space leads to generated solutions that remain close to the appropriate constraint manifold, indicating that the learned representation further captures geometric structure of the constraint family beyond intrinsic dimension alone. Constrained IK therefore offers a controlled setting for studying the intrinsic geometry learned by diffusion models.
