Despite today's prevalence of ultrasound imaging in medicine, ultrasound signal-to-noise ratio is still affected by several sources of noise and artefacts. Moreover, enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. Recently, there has been progress in both model-based and learning-based approaches addressing the problem of ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid reconstruction method combining an ultrasound linear direct model with a learning-based prior coming from a generative Denoising Diffusion model. More specifically, we rely on the unsupervised fine-tuning of a pre-trained Denoising Diffusion Restoration Model (DDRM). Given the nature of multiplicative noise inherent to ultrasound, this paper proposes an empirical model to characterize the stochasticity of diffusion reconstruction of ultrasound images, and shows the interest of its variance as an echogenicity map estimator. We conduct experiments on synthetic, in-vitro, and in-vivo data, demonstrating the efficacy of our variance imaging approach in achieving high-quality image reconstructions from single plane-wave acquisitions and in comparison to state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUSvar