A diffusion model learns to reverse a fixed noise-adding process by training a neural network to denoise step-by-step

Denoising Diffusion Probabilistic Models (DDPMs) work via two processes: a fixed forward process q that gradually adds Gaussian noise to a real image over T timesteps until it becomes pure noise, and a learned reverse process p_theta that a neural network is trained to invert — starting from pure noise and recovering a realistic image step by step. The forward process is predefined and requires no learning; the reverse process is what the model trains. At inference, you sample random Gaussian noise and iteratively apply the learned denoising network T times. Both processes are indexed by timestep t, and T is typically set to 1000. The key insight is that while the reverse conditional distribution p(x_{t-1}|x_t) is intractable to compute analytically, a neural network can approximate it.

Examples

Forward: sample real image, add Gaussian noise 1000 times → pure noise. Reverse: start from noise, run trained denoiser 1000 times → novel realistic image. The DDPM paper trained on image datasets; the tutorial trains on Fashion-MNIST in PyTorch.

Assessment

Describe the role of each process (forward vs. reverse) and explain why the forward process needs no training while the reverse does. Identify the direction of inference (reverse only).