Diffusion models have become the backbone of modern image generation, but the core idea isn’t new. The concept traces back to Sohl-Dickstein et al. in 2015, then got its breakthrough at Stanford with Song et al. in 2019 before Ho et al. at Google Brain refined it into the Denoising Diffusion Probabilistic Model (DDPM) in 2020 that most practitioners know today.
The setup is surprisingly straightforward compared to GANs or VAEs. You have two processes working in opposite directions. The forward process takes a real image and progressively destroys it by adding Gaussian noise over T timesteps, following a predetermined variance schedule. After enough steps, what remains is pure isotropic Gaussian noise. The reverse process is where the magic happens: a neural network learns to undo this destruction, gradually denoising from pure noise back to a coherent image.
The mathematical challenge is that the reverse conditional distribution is intractable—you’d need to know the distribution of all possible images to compute it exactly. So the neural network approximates it instead. The DDPM authors made a key simplifying choice: they fixed the variance schedule and let the network only learn the mean of the reverse conditional distribution. As the paper notes, both trainable and fixed variance approaches produced similar results experimentally.
What makes this framework elegant is that the forward process requires no learning at all. It’s a fixed, predefined noising schedule—linear, quadratic, or cosine—that gradually corrupts the data. The network’s entire job is learning to reverse that corruption. This is a stark contrast to GANs, where generator and discriminator are locked in an adversarial arms race, or Normalizing Flows, which require invertible architectures with tractable Jacobians. Diffusion sidesteps those constraints entirely, which helps explain why it has become the default approach for image synthesis in the years since DDPM was published.
