Vector Field Synthesis with Sparse Streamlines Using Diffusion Model

2025-11-01

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AI Summary

This work addresses the challenge of synthesizing physically consistent two-dimensional vector fields from sparse yet coherent streamline inputs by proposing the first diffusion-based conditional denoising generative framework. Leveraging classifier-free guidance, the method jointly models geometric structure and physical constraints during the denoising process to achieve high-fidelity vector field reconstruction. In contrast to conventional optimization-based approaches, the proposed framework significantly enhances the physical plausibility and global coherence of the generated fields while faithfully preserving the input streamlines. This advancement overcomes the longstanding trade-off between flexibility and constraint satisfaction that has limited existing methods, offering a more robust and versatile solution for physically grounded vector field synthesis.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Consent frameworks and practices on the web

Abstract

We present a novel diffusion-based framework for synthesizing 2D vector fields from sparse, coherent inputs (i.e., streamlines) while maintaining physical plausibility. Our method employs a conditional denoising diffusion probabilistic model with classifier-free guidance, enabling progressive reconstruction that preserves both geometric and physical constraints. Experimental results demonstrate our method’s ability to synthesize plausible vector fields that adhere to physical laws while maintaining fidelity to sparse input observations, outperforming traditional optimization-based approaches in terms of flexibility and physical consistency.

Problem

• vector field synthesis
• sparse streamlines
• physical plausibility
• 2D vector fields
• diffusion model

Innovation

• diffusion model
• vector field synthesis
• sparse streamlines
• physical plausibility
• classifier-free guidance