Noise Schedule
Controls
What are Diffusion Models?
Diffusion models are generative models that learn to produce data by reversing a gradual noising process. They have achieved state-of-the-art results in image generation (DALL-E 2, Stable Diffusion, Midjourney).
Forward Process
The forward process gradually adds Gaussian noise to data over T timesteps until it becomes pure noise. This destroys all structure in the data.
Reverse Process
The reverse process learns to denoise: starting from pure noise, a neural network predicts and removes noise at each step, gradually recovering the original data distribution.
How to Use
- Choose a distribution to set the data shape
- Run Forward to watch noise destroy structure
- Run Reverse to watch data emerge from noise
- Use Step to advance one timestep at a time
- Adjust steps to control the diffusion granularity
Forward Diffusion
At each timestep t, noise is added according to a variance schedule βt:
q(xt | xt-1) = N(xt; √(1 - βt) xt-1, βt I)
Each step mixes the current sample with a small amount of Gaussian noise.
Reverse Denoising
A neural network εθ is trained to predict the noise added at each step:
pθ(xt-1 | xt) = N(xt-1; μθ(xt, t), σt² I)
The model predicts the mean μθ of the denoised distribution.
Training Objective
The model is trained to predict the noise ε that was added:
L = E[ || ε - εθ(√α̅t x0 + √(1 - α̅t) ε, t) ||² ]
Simple MSE loss between actual and predicted noise.
Noise Schedule
βt = linear schedule from β1 to βT
αt = 1 - βt
α̅t = ∏s=1t αs
α̅t (alpha-bar) controls the total noise at step t. It decreases from 1 (clean) to ~0 (pure noise).
Closed-Form Forward
q(xt | x0) = N(xt; √α̅t x0, (1 - α̅t) I)
We can jump to any timestep t directly without iterating.
Evidence Lower Bound (ELBO)
log p(x) ≥ Eq[ log p(x0|x1) - Σt DKL(q(xt-1|xt,x0) || pθ(xt-1|xt)) ]
The training maximizes a variational lower bound on the log-likelihood.
Diffusion Status
| Current Step | 0 |
| Total Steps | 50 |
| Process | Forward |
| Noise Level (α̅t) | 1.000 |
| Distribution | Swiss Roll |
| Status | Ready |