| Abstract: |
| Abstract: We present a supervised learning framework for training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, and variational auto-encoders, are usually considered unsupervised learning models because labeled data are generally unavailable for training. Despite the success of the generative models, there are several issues with unsupervised training, e.g., the requirement of reversible architectures, vanishing gradients, and training instability. We utilize the score-based diffusion model to generate labeled data to enable supervised learning in generative models. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE) corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer high accuracy and substantial time savings in neural network training. Both algorithm development and convergence analysis will be presented. |
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