Ultrasound coherent plane wave compounding (CPWC) enables high frame-rate imaging by coherently summing echoes acquired at multiple steering angles. While CPWC is fast, using only a small number of steering angles makes the images prone to strong speckle noise and angle-related artifacts, which can obscure important anatomical details. Traditional denoising methods often reduce noise at the cost of blurring fine structures. To address this limitation, previous work has been done based on denoising diffusion probabilistic models (DDPM), which rely on Gaussian assumptions.
In this paper, we show that the noise, in the case of a small number of compounded angles, is not well described by the commonly assumed Gaussian model; instead, it has heavy-tailed, non-Gaussian characteristics that are better captured by a Laplacian distribution. Based on this observation, we incorporate this Laplacian noise model directly into the sampling process of a denoising diffusion implicit model (DDIM). We further propose a fast denoising method based on an adaptive diffusion time step estimation from noisy inputs. Applying the technique to both experimental and \emph{in vivo} carotid datasets shows that the proposed method enhances contrast and cyst visibility, as measured by the generalized contrast-to-noise ratio (gCNR). In particular, the results indicate that the number of transmissions can be reduced by 90% while achieving a gCNR comparable to that obtained with the maximum number of plane waves (PWs).