  FRAME (Filters, Random fields, And Maximum Entropy) is an energy-based
descriptive model that synthesizes visual realism by capturing mutual patterns
from structural input signals. The maximum likelihood estimation (MLE) is
applied by default, yet conventionally causes the unstable training energy that
wrecks the generated structures, which remains unexplained. In this paper, we
provide a new theoretical insight to analyze FRAME, from a perspective of
particle physics ascribing the weird phenomenon to KL-vanishing issue. In order
to stabilize the energy dissipation, we propose an alternative Wasserstein
distance in discrete time based on the conclusion that the
Jordan-Kinderlehrer-Otto (JKO) discrete flow approximates KL discrete flow when
the time step size tends to 0. Besides, this metric can still maintain the
model's statistical consistency. Quantitative and qualitative experiments have
been respectively conducted on several widely used datasets. The empirical
studies have evidenced the effectiveness and superiority of our method.
