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Diffusion Models: Probabilistic Image Reconstruction

Diffusion models operate on iterative denoising processes to generate high-quality images. The forward diffusion process adds noise to an image in small increments, progressively degrading it until only Gaussian noise remains. The reverse diffusion process reconstructs the image by predicting and removing noise at each step.

Key mathematical formulations in diffusion models include:

• Noise Scheduling – The function controlling the rate of noise addition and removal, often parameterized as β_t and α_t, where t represents the diffusion timestep.
• Variational Inference – Optimization of the probability distribution used to predict clean images from noisy inputs, minimizing the Kullback-Leibler divergence between predicted and actual distributions.
• U-Net Architectures – The backbone of diffusion-based models, featuring downsampling (encoder) and upsampling (decoder) layers with skip connections to retain fine-grained details.

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