Knowledge distillation (KD) aims to train a lightweight classifier suitable to provide accurate inference with constrained resources in multi-label learning. Instead of directly consuming feature-label pairs, the classifier is trained by a teacher, i.e., a high-capacity model whose training may be resource-hungry. The accuracy of the classifier trained this way is usually suboptimal because it is difficult to learn the true data distribution from the teacher. An alternative method is to adversarially train the classifier against a discriminator in a two-player game akin to generative adversarial networks (GAN), which can ensure the classifier to learn the true data distribution at the equilibrium of this game. However, it may take excessively long time for such a two-player game to reach equilibrium due to high-variance gradient updates.

The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a statistical viewpoint, illustrating that one can actually hope for improvement when models are trained on data contaminated with synthetic samples, as long as there is some amount of fresh information from the true target distribution. In particular, we consider iterative training on samples sourced from a mixture of the true target and synthetic distributions. We analyze the entire iterative evolution in a next-token prediction language model, capturing how the interplay between the mixture weights and the sample size controls the overall long-term performance. With non-trivial mixture weight of the true distribution, even if it decays over time, simply training the model in a contamination-agnostic manner with appropriate sample sizes can avoid collapse and even recover the true target distribution under certain conditions. Simulation studies support our findings and also show that such behavior is more general for other classes of models.

The past few years have witnessed great success in the use of diffusion models (DMs) to generate high-fidelity images with the help of stochastic differential equations (SDEs). However, discretization error is an inevitable limitation when utilizing numerical solvers to solve SDEs. To address this limitation, we provide a theoretical analysis demonstrating that an appropriate combination of the contrastive loss and score matching serves as an upper bound of the KL divergence between the true data distribution and the model distribution. To obtain this bound, we utilize a contrastive loss to construct a contrastive sampling chain to fine-tuning the pre-trained DM. In this manner, our method reduces the discretization error and thus yields a smaller gap between the true data distribution and our model distribution. Moreover, the presented method can be applied to fine-tuning various pre-trained DMs, both with or without fast sampling algorithms, contributing to better sample quality or slightly faster sampling speeds. To validate the efficacy of our method, we conduct comprehensive experiments. For example, on CIFAR10, when applied to a pre-trained EDM, our method improves the FID from 2.04 to 1.88 with 35 neural function evaluations (NFEs), and reduces NFEs from 35 to 25 to achieve the same 2.04 FID.

Generative Adversarial Nets (GANs) have shown promise in image generation and semi-supervised learning (SSL). However, existing GANs in SSL have two problems: (1) the generator and the discriminator (i.e. the classifier) may not be optimal at the same time; and (2) the generator cannot control the semantics of the generated samples.

Deep generative models provide powerful tools for distributions over complicated manifolds, such as those of natural images.

Knowledge distillation (KD) aims to train a lightweight classifier suitable to provide accurate inference with constrained resources in multi-label learning. Instead of directly consuming feature-label pairs, the classifier is trained by a teacher, i.e., a high-capacity model whose training may be resource-hungry. The accuracy of the classifier trained this way is usually suboptimal because it is difficult to learn the true data distribution from the teacher. An alternative method is to adversarially train the classifier against a discriminator in a two-player game akin to generative adversarial networks (GAN), which can ensure the classifier to learn the true data distribution at the equilibrium of this game. However, it may take excessively long time for such a two-player game to reach equilibrium due to high-variance gradient updates.

Neural Information Processing Systems http://nips.cc/

Recent diffusion-based generative models achieve remarkable results by training on massive datasets, yet this practice raises concerns about memorization and copyright infringement. A proposed remedy is to train exclusively on noisy data with potential copyright issues, ensuring the model never observes original content. However, through the lens of deconvolution theory, we show that although it is theoretically feasible to learn the data distribution from noisy samples, the practical challenge of collecting sufficient samples makes successful learning nearly unattainable. To overcome this limitation, we propose to pretrain the model with a small fraction of clean data to guide the deconvolution process. Combined with our Stochastic Forward--Backward Deconvolution (SFBD) method, we attain an FID of $6.31$ on CIFAR-10 with just $4\%$ clean images (and $3.58$ with $10\%$). Theoretically, we prove that SFBD guides the model to learn the true data distribution. The result also highlights the importance of pretraining on limited but clean data or the alternative from similar datasets. Empirical studies further support these findings and offer additional insights.

The past few years have witnessed great success in the use of diffusion models (DMs) to generate high-fidelity images with the help of stochastic differential equations (SDEs). However, discretization error is an inevitable limitation when utilizing numerical solvers to solve SDEs. To address this limitation, we provide a theoretical analysis demonstrating that an appropriate combination of the contrastive loss and score matching serves as an upper bound of the KL divergence between the true data distribution and the model distribution. To obtain this bound, we utilize a contrastive loss to construct a contrastive sampling chain to fine-tuning the pre-trained DM. In this manner, our method reduces the discretization error and thus yields a smaller gap between the true data distribution and our model distribution.

Neural Information Processing Systems http://nips.cc/