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Interactive 3D/Diffusion Process (DDPM)
Diffusion (DDPM)
Forward noise + reverse denoising
q(x_t|x_0) = N(√ᾱ_t x_0, (1−ᾱ_t)I)
Signal-to-Noise
t0 / 39
SNR>999
Noise0.0%
ᾱ_t1.0000
Scrub Timestep
t = 0 (clean)t = 0
datat = 39 (noise)
Animate
Schedule
T (timesteps)40
10100
β_start2.0e-4
1e-41e-2
β_end0.020
0.0100.050
Display
How It Works
Forward process adds Gaussian noise over T steps. At each step t, the data point moves toward a standard normal distribution.

Reverse process starts from pure noise and denoises step-by-step using the learned score function ∇log p(x_t).

The score arrows show the direction a trained network would push each noisy point to recover the original data distribution.

SNR = ᾱ_t / (1−ᾱ_t) → ∞ at t=0, → 0 at t=T
Legend
Cluster 1 (top)
Cluster 2 (right)
Cluster 3 (bottom)
Cluster 4 (left)
→Score ∇log p(x_t)

Diffusion Process (DDPM) - Interactive Visualization

Denoising Diffusion Probabilistic Models (DDPM) define two Markov chains: a fixed forward process that gradually adds Gaussian noise over T timesteps until the data is pure noise, and a learned reverse process that denoises step by step. A neural network is trained to predict the noise added at each step - equivalently, to estimate the score function (gradient of the log data density). Sampling requires running the full reverse chain.

  • Step through the forward process T=1000 timesteps: watch clean data dissolve into pure Gaussian noise
  • See the noise schedule: beta_t controls how much noise is added at each step - linear, cosine, and learned schedules compared
  • Watch the reverse process: the neural network iteratively denoises, each step recovering a slightly cleaner sample
  • Understand the training objective: predict the noise epsilon added at step t, equivalent to minimizing a reweighted ELBO
  • Learn why diffusion models produce better samples than GANs: they optimize a stable likelihood-based objective with no adversarial dynamics

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.