用几何监督生成精准互动手印，助力印度古典舞传承

Automatic generation of hand gestures is essential for the transmission of Indian classical dance and critical for its preservation. Indian classical dance gesture datasets are inherently low-resource, and the canonical Sanskrit definitions of many mudras lack precise textual descriptions, limiting the effectiveness of conventional text-conditioned image generation models. We present \textbf{MudraGen}, a conditional diffusion framework that synthesizes realistic RGB images of \textit{Samyukta Hasta Mudras} -- interactive two-hand gestures from Bharatanatyam (an Indian classical dance form). Unlike prior work on simple hand signs or single-hand gestures, MudraGen introduces geometry-aware supervision to capture the precise coordination, anatomical validity, and cultural nuance of interacting hands. We formulate three geometry-aware objectives: Keypoint Loss for 3D joint alignment, Joint Offset Loss for inter-hand spatial coherence, and Shape Consistency, which serves as an anatomical regularizer by encouraging consistent hand morphology while allowing independent hand poses. Together, these objectives guide the diffusion model toward anatomically plausible and well-coordinated hand configurations, enabling the synthesis of photorealistic and pose-accurate gesture images. Experimental results show that MudraGen surpasses existing state-of-the-art generative approaches in visual realism, anatomical correctness, and preservation of fine hand-pose structure, enabling faithful reproduction of complex Samyukta Hasta mudras. Beyond quantitative gains, its ability to generate culturally grounded and structurally consistent gestures highlights practical applications in cultural preservation and dance education.