Rui Gao

Peiyu Yu, Dinghuai Zhang, Hengzhi He et al.

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 (\ie, 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 ImageNet64x64 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.

Yaxuan Zhu, Zehao Dou, Haoxin Zheng et al.

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure using Tweedie's formula. Despite the merits of being versatile in solving various inverse problems without re-training, the performance of DPS is hindered by the fact that this posterior approximation can be inaccurate especially for high noise levels. Therefore, we propose \textbf{D}iffusion \textbf{P}osterior \textbf{MC}MC (\textbf{DPMC}), a novel inference algorithm based on Annealed MCMC to solve inverse problems with pretrained diffusion models. We define a series of intermediate distributions inspired by the approximated conditional distributions used by DPS. Through annealed MCMC sampling, we encourage the samples to follow each intermediate distribution more closely before moving to the next distribution at a lower noise level, and therefore reduce the accumulated error along the path. We test our algorithm in various inverse problems, including super resolution, Gaussian deblurring, motion deblurring, inpainting, and phase retrieval. Our algorithm outperforms DPS with less number of evaluations across nearly all tasks, and is competitive among existing approaches.