Over the several recent years, there has been a boom in development of flow
matching methods for generative modeling. One intriguing property pursued by
the community is the ability to learn flows with straight trajectories which
realize the optimal transport (OT) displacements. Straightness is crucial for
fast integration of the learned flow's paths. Unfortunately, most existing flow
straightening methods are based on non-trivial iterative procedures which
accumulate the error during training or exploit heuristic minibatch OT
approximations. To address this issue, we develop a novel optimal flow matching
approach which recovers the straight OT displacement for the quadratic cost in
just one flow matching step.

发展流匹配方法用于生成模型，追求流的直线轨迹，实现最优输运位移；文章提出一种新颖的最优流匹配方法，在一步流匹配中恢复二次成本下的直线输运位移。

最佳流匹配：一步学习直线轨迹

Optimal Flow Matching: Learning Straight Trajectories in Just One Step

Simulation-based inference (SBI) is constantly in search of more expressive
algorithms for accurately inferring the parameters of complex models from noisy
data. We present consistency models for neural posterior estimation (CMPE), a
new free-form conditional sampler for scalable, fast, and amortized SBI with
generative neural networks. CMPE combines the advantages of normalizing flows
and flow matching methods into a single generative architecture: It essentially
distills a continuous probability flow and enables rapid few-shot inference
with an unconstrained architecture that can be tailored to the structure of the
estimation problem. Our empirical evaluation demonstrates that CMPE not only
outperforms current state-of-the-art algorithms on three hard low-dimensional
problems, but also achieves competitive performance in a high-dimensional
Bayesian denoising experiment and in estimating a computationally demanding
multi-scale model of tumor spheroid growth.

基于模拟的推断（SBI）不断寻找更具表现力的算法，以准确地从嘈杂的数据中推断出复杂模型的参数。我们提出了神经后验估计的一致性模型（CMPE），这是一种用于可扩展、快速和分摊的 SBI 的新型无限制条件采样器，具有生成式神经网络。CMPE 将正态流和流匹配方法的优点融合到一个单一的生成式架构中：它本质上提炼出一个连续概率流，并能够通过一个未受限制的架构进行快速的少样本推断，以适应估计问题的结构。我们的实证评估证明，CMPE 不仅在三个困难的低维问题上优于当前最先进的算法，而且在高维贝叶斯去噪实验和对计算要求严格的肿瘤球体生长的多尺度模型估计中也取得了竞争性的性能。

大规模和快速基于仿真的推论的一致性模型

Consistency Models for Scalable and Fast Simulation-Based Inference

Score-based generative models are a popular class of generative modelling
techniques relying on stochastic differential equations (SDE). From their
inception, it was realized that it was also possible to perform generation
using ordinary differential equations (ODE) rather than SDE. This led to the
introduction of the probability flow ODE approach and denoising diffusion
implicit models. Flow matching methods have recently further extended these
ODE-based approaches and approximate a flow between two arbitrary probability
distributions. Previous work derived bounds on the approximation error of
diffusion models under the stochastic sampling regime, given assumptions on the
$L^2$ loss. We present error bounds for the flow matching procedure using fully
deterministic sampling, assuming an $L^2$ bound on the approximation error and
a certain regularity condition on the data distributions.

本文提出了一种使用完全确定性采样的流匹配过程，该过程利用概率流 ODE 方法和去噪扩散隐式模型，为基于 ODE 的生成模型提供了误差界限。