用布朗运动提升超分辨率，让图像更真实、边缘更清晰。

Diffusion-model-based image super-resolution techniques often face a trade-off between realistic image generation and computational efficiency. This issue is exacerbated when inference times by decreasing sampling steps, resulting in less realistic and hazy images. To overcome this challenge, we introduce a novel diffusion model named PixelBoost that underscores the significance of embracing the stochastic nature of Brownian motion in advancing image super-resolution, resulting in a high degree of realism, particularly focusing on texture and edge definitions. By integrating controlled stochasticity into the training regimen, our proposed model avoids convergence to local optima, effectively capturing and reproducing the inherent uncertainty of image textures and patterns. Our proposed model demonstrates superior objective results in terms of learned perceptual image patch similarity (LPIPS), lightness order error (LOE), peak signal-to-noise ratio(PSNR), structural similarity index measure (SSIM), as well as visual quality. To determine the edge enhancement, we evaluated the gradient magnitude and pixel value, and our proposed model exhibited a better edge reconstruction capability. Additionally, our model demonstrates adaptive learning capabilities by effectively adjusting to Brownian noise patterns and introduces a sigmoidal noise sequencing method that simplifies training, resulting in faster inference speeds.