Diffusion Model Simulator | mysimulator.uk

Image pattern

Diffusion schedule

Diffusion steps T 40

β schedule steepness 1.0×

Playback

Playback speed 6 steps/s

Timestep

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Noise level

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ᾱ_t (signal kept)

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β_t (this step)

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How it works

Each grid point holds a scalar "pixel" value x₀ ∈ {−1,+1} defining a clean pattern (cross / circle / ring). The forward diffusion process corrupts it step by step by mixing in Gaussian noise ε, and thanks to the reparameterisation trick the state at any timestep t can be reached in one shot, without simulating every intermediate step:

x_t = √(ᾱ_t)·x₀ + √(1 − ᾱ_t)·ε
ᾱ_t = ∏ᵢ₌₁ᵗ (1 − βᵢ)

β follows a linear noise schedule from β_min to β_max·steepness across T steps. As t grows, ᾱ_t shrinks toward 0, so the √ᾱ_t·x₀ term (signal) fades out while the √(1−ᾱ_t)·ε term (noise) takes over — the pattern dissolves into static. The reverse process plays the exact same precomputed sequence backward: from pure noise at t=T back to the clean pattern at t=0, which is what a trained denoiser learns to approximate step-by-step in a real model.

Diffusion steps T — how many discrete noise levels the schedule is divided into; more steps means a smoother, more gradual corruption/reconstruction.
β schedule steepness — scales β_max; a steeper schedule destroys the signal faster, reaching near-pure noise well before t=T.
Timestep scrubber — drag to jump straight to any point in the process and see x_t rendered instantly, in either direction.
Both ways — runs the forward pass 0→T then the reverse pass T→0, looping continuously.

Real-world relevance: this closed-form forward formula is exactly what models like DDPM, DDIM and Stable Diffusion use to generate a noisy training target at a random timestep in one step, and what an ODE/SDE sampler reverses — approximately, step by step — to turn pure noise into a photorealistic image.

t = 0 / 40

noise: 0%

ᾱ_t: 1.000

Scrub timestept = 0

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