A real diffusion model (DALL·E 2, Stable Diffusion) learns to reverse a gradual noising process: starting from pure noise, it repeatedly predicts and subtracts a little bit of noise until a coherent image emerges. This 2D visualizer follows the same update rule with a toy target instead of a trained network — every dot starts at a random point on the canvas and, each step, moves partway toward its assigned position on the target outline while a shrinking amount of random jitter is mixed back in, so the cloud visibly "denoises" from chaos into structure.
x(t−1) = x(t) − η·(x(t) − target) + σ(t)·ε
σ(t) = σ0 · (1 − t / T)
- Diffusion steps (T) — how many denoising steps the generation takes; more steps trace a smoother path from noise to form.
- Noise strength (σ0) — how much random jitter ε is mixed in early on; higher values keep the cloud chaotic for longer before it resolves.
- Denoise speed — playback rate of the step loop, so you can slow down and watch a single step's pull-toward-target + jitter clearly.
- Target shape — the "prompt": the fixed point outline (circle / ring / spiral) every dot is guided toward, standing in for whatever a trained model would predict.
Real-world relevance: this same predict-and-subtract loop, run thousands of times on trained noise predictors, is what actually powers today's image, video and audio generators — the toy version here keeps the geometry but swaps the neural network for a fixed target.