A synthetic RMT intuition builder

Same noise. Different training. One strange convergence.

Hold the latent seed fixed. Change how strongly two synthetic denoisers share dominant spectral directions. Then measure what their outputs actually have in common.

Open the labSee the mechanism
ONE LATENT / TWO PATHSMEASURED, NOT MEMORIZED

Keep the noise. Move the spectrum.

The outputs below are generated in your browser. Similarity and overlap are calculated from the rendered arrays, not prewritten values.

Model ADataset: contours
Model BDataset: textures
0%Pixel cosine similarity
0%Dominant mode overlap

Preparing the shared latent...

Conceptual synthetic simulator. It illustrates the shared-spectrum mechanism named in the post; it does not reproduce the cited paper, its datasets, or a trained diffusion model.

Why the same seed can rhyme twice.

Random matrices can have universal large-scale spectral behavior even when their microscopic entries differ. In this lab, the analogy becomes visible.

FIX THE INPUT

The seed is a coordinate.

A seed deterministically selects the initial noise. Both paths begin at the same point, so changing the seed moves both through the same latent coordinate system.

SHARE THE STRONG DIRECTIONS

Dominant modes steer structure.

When high-energy spectral directions align, broad composition can converge even while dataset-specific textures remain different.

LET DENOISING AMPLIFY

Structure wins the iteration.

More denoising steps strengthen shared low-frequency structure. Lower alignment lets distinct training textures dominate instead.

Universality

Different random systems can share stable macroscopic spectral patterns. That is the conceptual bridge behind this experiment.

Not memorization

Matching structure does not by itself show that either path stored an image. Here, every pixel is constructed from the current seed and controls.

Not a paper replica

This is a teaching model, not evidence about the exact ICML result. It makes one proposed mechanism inspectable and falsifiable inside the toy system.

SHARED SEED   DOMINANT MODES   DIFFERENT TEXTURES   MEASURE THE OUTPUT   SHARED SEED   DOMINANT MODES   DIFFERENT TEXTURES   MEASURE THE OUTPUT  

Change one variable. Watch the agreement move.

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