Discrete Distribution Networks

Recent works have attempted to address this issue through zero-shot conditional generation (ZSCG). However, these methods either only support conditions in the same pixel domain as the training data Wang et al. (2022); Lugmayr et al. (2022); Meng et al. (2021); Nair et al. (2023) or depend on discriminative models to supply gradients during generation Yu et al. (2023). In contrast, DDN supports a wide range of ZSCG tasks, encompassing both pixel-domain and non-pixel-domain conditions, as shown in fig. 2. To the best of our knowledge, DDN is the first generative model capable of performing zero-shot conditional generation in non-pixel domains without relying on gradient information. This implies that DDN can achieve ZSCG solely based on black-box discriminative models.

The core concept of Discrete Distribution Networks (DDN) is to approximate the distribution of training data using a multitude of discrete sample points. The secret to generating diverse samples lies in the network's ability to concurrently generate multiple samples (K). This is perceived as the network outputting a discrete distribution. All generated samples serve as the sample space for this discrete distribution. Typically, each sample in this discrete distribution has an equal probability mass of 1/K. Our goal is to make this discrete distribution as close as possible to the target dataset.

To accurately fit the target distribution of large datasets, a substantial representational space is required. In the most extreme scenario, this space must be larger than the number of training data samples. However, current neural networks lack the feasibility to generate such a vast number of