Generative modelling over continuous-time geometric constructs, a.k.a such as
handwriting, sketches, drawings etc., have been accomplished through
autoregressive distributions. Such strictly-ordered discrete factorization
however falls short of capturing key properties of chirographic data -- it
fails to build holistic understanding of the temporal concept due to one-way
visibility (causality). Consequently, temporal data has been modelled as
discrete token sequences of fixed sampling rate instead of capturing the true
underlying concept. In this paper, we introduce a powerful model-class namely
"Denoising Diffusion Probabilistic Models" or DDPMs for chirographic data that
specifically addresses these flaws. Our model named "ChiroDiff", being
non-autoregressive, learns to capture holistic concepts and therefore remains
resilient to higher temporal sampling rate up to a good extent. Moreover, we
show that many important downstream utilities (e.g. conditional sampling,
creative mixing) can be flexibly implemented using ChiroDiff. We further show
some unique use-cases like stochastic vectorization, de-noising/healing,
abstraction are also possible with this model-class. We perform quantitative
and qualitative evaluation of our framework on relevant datasets and found it
to be better or on par with competing approaches.

本文介绍了一种名为 “ChiroDiff” 的非自回归模型，它学会了捕捉整体概念，能够更好地处理手写、素描等实时几何构造数据，并且还能够灵活地实现很多重要的下游应用。研究表明，该模型在相关数据集中的定量与定性评估中表现良好，并且能够更好地或达到竞争对手的水平。

利用扩散模型对手写数据进行建模

ChiroDiff: Modelling chirographic data with Diffusion Models

Applications from finance to epidemiology and cyber-security require accurate
forecasts of dynamic phenomena, which are often only partially observed. We
demonstrate that a system's predictability degrades as a function of temporal
sampling, regardless of the adopted forecasting model. We quantify the loss of
predictability due to sampling, and show that it cannot be recovered by using
external signals. We validate the generality of our theoretical findings in
real-world partially observed systems representing infectious disease
outbreaks, online discussions, and software development projects. On a variety
of prediction tasks---forecasting new infections, the popularity of topics in
online discussions, or interest in cryptocurrency projects---predictability
irrecoverably decays as a function of sampling, unveiling fundamental
predictability limits in partially observed systems.

本研究研究了部分观测系统中的预测性能，并证明了时间采样导致的不确定性损失是无法通过使用外部信号进行补偿的，证实了这一理论的适用性。同时还考察了实际系统中的感染疾病、在线讨论以及软件开发等方面，发现随着时间采样的增加，部分系统的可预测性会出现不可逆的下降，揭示了部分观测系统中的基本可预测性限制。