# Efficiency vs. Fidelity: A Comparative Analysis of Diffusion Probabilistic Models and Flow Matching on Low-Resource Hardware

arXiv: https://arxiv.org/abs/2511.19379 · HTML: https://mlsanity.com/paper/2511.19379/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 4 of its 5 references that are in the map.
- First posted on arXiv 24 Nov 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 4 of 4)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)

## Built on by (most cited first, 1 of 1)

- [Wavelet Flow Matching for Multi-Scale Physics Emulation](https://mlsanity.com/paper/2605.16573/) (2026)

## Abstract (arXiv)

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 C ≈ 1.02), which is near-optimal, whereas Diffusion trajectories remain stochastic and tortuous (C ≈ 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. This work concludes that Flow Matching is the superior algorithmic choice for real-time, resource-constrained generative tasks.