Straightening the probability flow of the continuous-time generative models,
such as diffusion models or flow-based models, is the key to fast sampling
through the numerical solvers, existing methods learn a linear path by directly
generating the probability path the joint distribution between the noise and
data distribution. One key reason for the slow sampling speed of the ODE-based
solvers that simulate these generative models is the global truncation error of
the ODE solver, caused by the high curvature of the ODE trajectory, which
explodes the truncation error of the numerical solvers in the low-NFE regime.
To address this challenge, We propose a novel method called SeqRF, a learning
technique that straightens the probability flow to reduce the global truncation
error and hence enable acceleration of sampling and improve the synthesis
quality. In both theoretical and empirical studies, we first observe the
straightening property of our SeqRF. Through empirical evaluations via SeqRF
over flow-based generative models, We achieve surpassing results on CIFAR-10,
CelebA-$64 \times 64$, and LSUN-Church datasets.

SeqRF 是一种学习技术，通过改善概率流的直线性来减少全局截断误差，加速采样并提高合成质量。在理论和实证研究中，我们观察到了 SeqRF 的直线性属性，并通过 SeqRF 在基于流模型的生成模型上进行的实证评估，在 CIFAR-10、CelebA-$64 	imes 64$ 和 LSUN-Church 数据集上取得了优异的结果。

生成模型的顺序流匹配

Sequential Flow Matching for Generative Modeling

Continuous diffusion models are commonly acknowledged to display a
deterministic probability flow, whereas discrete diffusion models do not. In
this paper, we aim to establish the fundamental theory for the probability flow
of discrete diffusion models. Specifically, we first prove that the continuous
probability flow is the Monge optimal transport map under certain conditions,
and also present an equivalent evidence for discrete cases. In view of these
findings, we are then able to define the discrete probability flow in line with
the principles of optimal transport. Finally, drawing upon our newly
established definitions, we propose a novel sampling method that surpasses
previous discrete diffusion models in its ability to generate more certain
outcomes. Extensive experiments on the synthetic toy dataset and the CIFAR-10
dataset have validated the effectiveness of our proposed discrete probability
flow. Code is released at:
this https URL

本文旨在建立离散扩散模型的概率流动基本理论，从而定义符合最优运输原理的离散概率流动，并提出一种超越以往的离散扩散模型的新型采样方法。通过在合成玩具数据集和 CIFAR-10 数据集上的广泛实验证实了所提出的离散概率流动的有效性。

离散概率流通过最优传输的构建

Formulating Discrete Probability Flow Through Optimal Transport

The Hopfield recurrent neural network is a classical auto-associative model
of memory, in which collections of symmetrically-coupled McCulloch-Pitts
neurons interact to perform emergent computation. Although previous researchers
have explored the potential of this network to solve combinatorial optimization
problems and store memories as attractors of its deterministic dynamics, a
basic open problem is to design a family of Hopfield networks with a number of
noise-tolerant memories that grows exponentially with neural population size.
Here, we discover such networks by minimizing probability flow, a recently
proposed objective for estimating parameters in discrete maximum entropy
models. By descending the gradient of the convex probability flow, our networks
adapt synaptic weights to achieve robust exponential storage, even when
presented with vanishingly small numbers of training patterns. In addition to
providing a new set of error-correcting codes that achieve Shannon's channel
capacity bound, these networks also efficiently solve a variant of the hidden
clique problem in computer science, opening new avenues for real-world
applications of computational models originating from biology.

通过最小化概率流量，设计出一种具有指数级噪声容忍内存的 Hopfield 循环神经网络，该网络不仅能够实现 Shannon 信道容量界限，还可以高效地解决计算机科学中的隐藏社团问题，为来自生物学的计算模型的实际应用敞开了新的大门。