Denoising Diffusion Probabilistic Models (DDPMs) have established a new state-of-the-art in generative image synthesis, yet their deployment is hindered by significant computational overhead during inference, often requiring up to 1,000 iterative steps. This study presents a rigorous comparative analysis of DDPMs against the emerging Flow Matching (Rectified Flow) paradigm, specifically isolating their geometric and efficiency properties on low-resource hardware. By implementing both frameworks on a shared Time-Conditioned U-Net backbone using the MNIST dataset, we demonstrate that Flow Matching significantly outperforms Diffusion in efficiency. Our geometric analysis reveals that Flow Matching learns a highly rectified transport path (Curvature $\mathcal{C} \approx 1.02$), which is near-optimal, whereas Diffusion trajectories remain stochastic and tortuous ($\mathcal{C} \approx 3.45$). Furthermore, we establish an ``efficiency frontier'' at $N=10$ function evaluations, where Flow Matching retains high fidelity while Diffusion collapses. Finally, we show via numerical sensitivity analysis that the learned vector field is sufficiently linear to render high-order ODE solvers (Runge-Kutta 4) unnecessary, validating the use of lightweight Euler solvers for edge deployment. \textbf{This work concludes that Flow Matching is the superior algorithmic choice for real-time, resource-constrained generative tasks.}

翻译：去噪扩散概率模型（DDPMs）已在生成式图像合成领域确立了新的最先进水平，但其部署受到推理过程中显著计算开销的阻碍，通常需要多达1,000次迭代步骤。本研究对DDPMs与新兴的流匹配（整流流）范式进行了严格的对比分析，特别聚焦于它们在低资源硬件上的几何与效率特性。通过在MNIST数据集上使用共享的时间条件U-Net主干网络实现两种框架，我们证明流匹配在效率上显著优于扩散模型。我们的几何分析表明，流匹配学习到高度整流的传输路径（曲率$\mathcal{C} \approx 1.02$），接近最优，而扩散轨迹则保持随机且曲折（$\mathcal{C} \approx 3.45$）。此外，我们在$N=10$次函数评估处建立了一个“效率边界”，其中流匹配保持高保真度，而扩散模型则性能崩溃。最后，通过数值敏感性分析，我们证明学习到的向量场具有足够的线性度，使得高阶ODE求解器（如龙格-库塔四阶方法）变得不必要，从而验证了轻量级欧拉求解器在边缘部署中的适用性。\textbf{本工作得出结论：对于实时、资源受限的生成任务，流匹配是更优的算法选择。}