One fascinating aspect of pre-trained Audio-Language Models (ALMs) learning is their impressive zero-shot generalization capability and test-time adaptation (TTA) methods aiming to improve domain performance without annotations. However, previous test time adaptation (TTA) methods for ALMs in zero-shot classification tend to be stuck in incorrect model predictions. In order to further boost the performance, we propose multiple guidance on prompt learning without annotated labels. First, guidance of consistency on both context tokens and domain tokens of ALMs is set. Second, guidance of both consistency across multiple augmented views of each single test sample and contrastive learning across different test samples is set. Third, we propose a corresponding end-end learning framework for the proposed test-time adaptation method without annotated labels. We extensively evaluate our approach on 12 downstream tasks across domains, our proposed adaptation method leads to 4.41% (max 7.50%) average zero-shot performance improvement in comparison with the state-of-the-art models.

We propose a generalized score-based diffusion framework for learning multivariate Gaussian mixture models with homoscedastic or heteroscedastic noise. Our goal is to nonparametrically estimate the latent location distribution and denoise the observations. Departing from the conventional maximum likelihood approach, we reinterpret each observation as a temporal slice of a family of stochastic diffusion processes. This modeling choice enables a principled characterization of the additive noise structure and supports a multi-step denoising procedure grounded in reverse-time dynamics. We introduce a score-based objective that explicitly models the latent distribution and accommodates observation-specific noise covariances. Theoretically, we establish that the score estimation error with $n$ independent observations achieves a near-parametric error rate of $\frac{\mathrm{polylog}(n)}{n}$, improving upon existing results in the diffusion literature. Empirically, our method outperforms the nonparametric maximum likelihood estimator in both density estimation and denoising fidelity, especially in high-dimensional settings. These findings suggest a promising direction for integrating nonparametric empirical Bayes with diffusion-based generative modeling for latent structure recovery.