``Noisier'’ Noise Contrastive Estimation is (Almost) Maximum Likelihood

Peiyu Yu, Dinghuai Zhang, Hengzhi He, Xiaojian Ma, Sirui Xie, RUIYAO MIAO, Yifan Lu, Yasi Zhang, Deqian Kong, Ruiqi Gao, Jianwen Xie, Guang Cheng, Ying Nian Wu

Keywords: Noise Contrastive Estimation; Generative Models

TL;DR: We revisit NCE through the lens of approximate maximum likelihood, showing that a noisier NCE better approximates MLE and provides strong methods for image modeling including distillation, anomaly detection, and offline black-box optimization.

Abstract: Noise Contrastive Estimation (NCE) has fueled major breakthroughs in representation learning and generative modeling. Yet a long-standing challenge remains: accurately estimating ratios between distributions that differ substantially, which significantly limits the applicability of NCE on modern high-dimensional and multimodal datasets. We revisit this problem from a less explored perspective: the magnitude of the noise distribution. Specifically, we show that with a virtually scaled (i.e., artificially increased) noise magnitude, the gradient of the NCE objective can closely align with that of Maximum Likelihood, enabling a trajectory-wise approximation from NCE to MLE, and faster convergence both theoretically and empirically. Building on this insight, we introduce "Noisier" NCE, a simple drop-in modification to vanilla NCE that incurs little to no extra computational cost, while effectively handling density-ratio estimation in challenging regimes where traditional MLE and NCE struggle. Beyond improving classical density-ratio learning, "Noisier" NCE proves broadly applicable: it achieves strong results across image modeling, anomaly detection, and offline black-box optimization. On CIFAR-10 and ImageNet64×64 datasets, it yields 10-step and even 1-step samplers that match or surpass state-of-the-art methods, while cutting training iterations by up to half.

Primary Area: generative models

Submission Number: 5294