Unsupervised deep learning methods for solving audio restoration problems extensively rely on carefully tailored neural architectures that carry strong inductive biases for defining priors in the time or spectral domain. In this context, lot of recent success has been achieved with sophisticated convolutional network constructions that recover audio signals in the spectral domain. However, in practice, audio priors require careful engineering of the convolutional kernels to be effective at solving ill-posed restoration tasks, while also being easy to train. To this end, in this paper, we propose a new U-Net based prior that does not impact either the network complexity or convergence behavior of existing convolutional architectures, yet leads to significantly improved restoration. In particular, we advocate the use of carefully designed dilation schedules and dense connections in the U-Net architecture to obtain powerful audio priors. Using empirical studies on standard benchmarks and a variety of ill-posed restoration tasks, such as audio denoising, in-painting and source separation, we demonstrate that our proposed approach consistently outperforms widely adopted audio prior architectures.