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.