We are interested in gradient-based Explicit Generative Modeling where samples can be derived from iterative gradient updates based on an estimate of the score function of the data distribution. Recent advances in Stochastic Gradient Langevin Dynamics (SGLD) demonstrates impressive results with energy-based models on high-dimensional and complex data distributions. Stein Variational Gradient Descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate a given distribution, based on functional gradient descent that decreases the KL divergence. SVGD has promising results on several Bayesian inference applications. However, applying SVGD on high dimensional problems is still under-explored. The goal of this work is to study high dimensional inference with SVGD. We first identify key challenges in practical kernel SVGD inference in high-dimension. We propose noise conditional kernel SVGD (NCK-SVGD), that works in tandem with the recently introduced Noise Conditional Score Network estimator. NCK is crucial for successful inference with SVGD in high dimension, as it adapts the kernel to the noise level of the score estimate. As we anneal the noise, NCK-SVGD targets the real data distribution. We then extend the annealed SVGD with an entropic regularization. We show that this offers a flexible control between sample quality and diversity, and verify it empirically by precision and recall evaluations. The NCK-SVGD produces samples comparable to GANs and annealed SGLD on computer vision benchmarks, including MNIST and CIFAR-10.
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