  Existing Score-Based Models (SBMs) can be categorized into constrained SBMs
(CSBMs) or unconstrained SBMs (USBMs) according to their parameterization
approaches. CSBMs model probability density functions as Boltzmann
distributions, and assign their predictions as the negative gradients of some
scalar-valued energy functions. On the other hand, USBMs employ flexible
architectures capable of directly estimating scores without the need to
explicitly model energy functions. In this paper, we demonstrate that the
architectural constraints of CSBMs may limit their modeling ability. In
addition, we show that USBMs' inability to preserve the property of
conservativeness may lead to degraded performance in practice. To address the
above issues, we propose Quasi-Conservative Score-Based Models (QCSBMs) for
keeping the advantages of both CSBMs and USBMs. Our theoretical derivations
demonstrate that the training objective of QCSBMs can be efficiently integrated
into the training processes by leveraging the Hutchinson's trace estimator. In
addition, our experimental results on the CIFAR-10, CIFAR-100, ImageNet, and
SVHN datasets validate the effectiveness of QCSBMs. Finally, we justify the
advantage of QCSBMs using an example of a one-layered autoencoder.
