Standard text-to-image diffusion sampling, as in Stable Diffusion v1, DALL·E 2 and Imagen, starts from random noise. Image editing can start from a noised input image, and the original DALL·E was autoregressive. In this video we build diffusion models from the ground up and see exactly how a neural network learns to turn noise into images.
We start with the forward process, which slowly destroys an image with Gaussian noise and can jump to any noise level in a single step. Then we reverse the arrow: a time-aware U-Net learns to undo the noise, one small Gaussian step at a time. You will see why the DDPM paper's key trick, predicting the noise instead of the image, reduces training to a simple mean squared error.
Next, a second lens: score matching. We connect noise prediction to the gradient of log-probability, from Hyvärinen's score matching and Vincent's denoising score matching to Langevin dynamics, noise-conditional score networks and the SDE framework.
Then DDPM vs. DDIM: how the same trained network can use far fewer steps with a deterministic sampler. The DDIM paper reported 10-50× wall-clock speedups in its experiments, with a quality, speed trade-off, and demonstrated interpolation and approximate inversion. Finally, latent diffusion, the architecture behind Stable Diffusion v1: an autoencoder represents 512×512×3 images as 64×64×4 latents, 48× fewer tensor values, diffusion runs in latent space, cross-attention connects text, and classifier-free guidance makes the model follow your prompt.
All formulas are shown on screen, with the idea behind each one explained in plain language.
We start with the forward process, which slowly destroys an image with Gaussian noise and can jump to any noise level in a single step. Then we reverse the arrow: a time-aware U-Net learns to undo the noise, one small Gaussian step at a time. You will see why the DDPM paper's key trick, predicting the noise instead of the image, reduces training to a simple mean squared error.
Next, a second lens: score matching. We connect noise prediction to the gradient of log-probability, from Hyvärinen's score matching and Vincent's denoising score matching to Langevin dynamics, noise-conditional score networks and the SDE framework.
Then DDPM vs. DDIM: how the same trained network can use far fewer steps with a deterministic sampler. The DDIM paper reported 10-50× wall-clock speedups in its experiments, with a quality, speed trade-off, and demonstrated interpolation and approximate inversion. Finally, latent diffusion, the architecture behind Stable Diffusion v1: an autoencoder represents 512×512×3 images as 64×64×4 latents, 48× fewer tensor values, diffusion runs in latent space, cross-attention connects text, and classifier-free guidance makes the model follow your prompt.
All formulas are shown on screen, with the idea behind each one explained in plain language.
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