What is the forward vs reverse process?

The forward process is a fixed procedure that gradually adds Gaussian noise to an image until it becomes indistinguishable from static — this defines the corruption. The reverse process is the learned part: a network trained to undo one step of noising at a time. Generation runs only the reverse process, starting from noise.

What does the model actually predict at each step?

In DDPM the network is trained to predict the noise that was added, given the noisy image and the timestep. Subtracting a scaled version of that predicted noise yields a slightly less noisy image. Repeating this over all timesteps turns pure noise into a sample from the data distribution.

LABS · 08 / DIFFUSION

Out of the Static.

Q: How do diffusion models generate images?

Diffusion models generate by reversing a noising process. Training corrupts real images into pure noise over many small steps; generation runs it backward — start from random Gaussian noise and, at each step, a neural network predicts the noise to remove, revealing a slightly cleaner image. After all the steps, a coherent image emerges from the static.

Q: What is the noise schedule?

The noise schedule sets how much noise is present at each timestep — high near the start (near pure static) and decreasing to zero at the end (a clean image). It controls the pace of both corruption and denoising, and choosing a good schedule matters for sample quality and speed.

Q: Why are diffusion models slow?

Because generation runs the network once per denoising step, and there can be dozens or hundreds of steps for one image — unlike a GAN's single pass. Faster samplers (like DDIM) cut the step count, and latent diffusion runs the process in a compressed space to make high-resolution generation affordable.

A diffusion model doesn't paint — it un-noises. Start with a screen of pure random pixels and, step by step, wipe away a little of the noise. Do it enough times and a picture climbs out of the static. Watch a shape appear from nothing.

THE GIST · 20 SECONDS

Training teaches a model to reverse a noising process: add a little Gaussian noise to real images over and over until they're pure static, and learn to undo one step. To generate, start from noise and run it backward — each step the model predicts the noise and removes a bit, revealing a cleaner image. After all steps, a picture emerges. That's DDPM.

Forwardadd noise (fixed)
Reverseremove noise (learned)
Schedulenoise: high → 0
Samplenoise → image

Hit Step to remove one round of noise — or Play and watch the picture climb out of the static.

UNDER THE HOOD

What you just played, written down

Corruption is easy and fixed; restoration is hard and learned. Diffusion trains a network to reverse noise one small step at a time — then runs that reversal from pure static to make something new.

How diffusion works — four moves

Forward (training only). Take a real image and add a little Gaussian noise, over and over, until it's pure static.
Learn to undo one step. Train a network to look at a noisy image and its timestep and predict the noise that was added.
Start from noise. To generate, begin with a fresh screen of random Gaussian noise — no image at all.
Denoise to a sample. Repeatedly predict and remove a bit of noise; after all timesteps, a coherent image emerges.

WHY NOISE, OF ALL THINGS?

Turning an image into noise is trivial and needs no learning — so it's a free source of training pairs. All the intelligence goes into the reverse step, and running that reverse process from scratch is how new images are born.

The reverse step in code

x = torch.randn(shape)              # start from pure noise
for t in reversed(range(T)):
    eps = model(x, t)               # predict the noise
    x = remove_noise(x, eps, t)     # take one step cleaner
    if t > 0:
        x = x + sigma(t) * torch.randn_like(x)
return x                            # a fresh sample

TRAININGpredict εthe noise added

SAMPLINGT stepsnoise → image

WHY IT'S SLOW — AND THE FIX

One network call per step, dozens to hundreds of steps per image. DDIM samplers cut the steps; latent diffusion (Stable Diffusion) runs the whole process in a compressed space to make it affordable.

⚠ This is a simplification

Here the noise simply fades toward a fixed target so you can see the emergence. A real model doesn't know the target — it learns to predict noise, and each denoise is a genuine neural-network step, not a scripted fade.

↔ How you steer it

Add a text prompt and the denoiser is conditioned on it (via cross-attention), so the image that emerges matches the words. That's text-to-image generation.

★ Where it's used

Stable Diffusion, DALL·E, Midjourney, and modern video and audio generators — diffusion is the dominant way to generate high-fidelity media.

QUICK CHECK

Did it stick?

FAQ

Diffusion, answered

How do diffusion models generate images?

By reversing a noising process: start from pure Gaussian noise and, at each step, a network predicts a little noise to remove, revealing a cleaner image. After all steps, a coherent image emerges from the static.

Forward vs reverse process?

Forward (fixed): gradually add noise to real images until they're static — used only in training. Reverse (learned): a network undoes one noising step at a time; generation runs this from noise.

What does the model predict?

In DDPM it predicts the noise that was added to a noisy image at a given timestep. Subtracting a scaled version of that noise gives a slightly cleaner image.

What is the noise schedule?

How much noise is present at each timestep — high near the start, dropping to zero at the end. It paces both the corruption and the denoising.

Why are diffusion models slow?

They call the network once per step, over many steps. DDIM cuts the step count and latent diffusion runs in a compressed space to speed things up.

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ML Foundations

Out of the Static.

What you just played, written down

How diffusion works — four moves

The reverse step in code

⚠ This is a simplification

↔ How you steer it

★ Where it's used

Did it stick?

Diffusion, answered

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What you just played, written down

How diffusion works — four moves

The reverse step in code

⚠ This is a simplification

↔ How you steer it

★ Where it's used

Did it stick?

Diffusion, answered

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