# Vector Field Synthesis with Sparse Streamlines Using Diffusion Model

arXiv: https://arxiv.org/abs/2604.09838 · HTML: https://mlsanity.com/paper/2604.09838/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [A guiding vector field algorithm for path following control of nonholonomic mobile robots](https://mlsanity.com/paper/1610.04391/) (2016)
- [Extract and Characterize Hairpin Vortices in Turbulent Flows](https://mlsanity.com/paper/2308.06283/) (2023)
- [Inpainting Computational Fluid Dynamics with Deep Learning](https://mlsanity.com/paper/2402.17185/) (2024)
- [Topological Separation of Vortices](https://mlsanity.com/paper/2407.03384/) (2024)

## Abstract (arXiv)

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.