FRAME Revisited: An Interpretation View Based on Particle Evolution

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.