Generative AI Latent Space Explorer

Latent Samples

Interpolation

Path position t 0%

Sampling

Temperature σ 0.00

Decoder State

z(t) = (0.00, 0.00, 0.00)

‖z(t)‖ (latent norm)

0.00

Relative likelihood

100%

How it works

Generative models (GANs, VAEs, diffusion models) don't store outputs — they learn a smooth decoder function G that maps points in a compressed latent space to full outputs (images, audio, text embeddings). Points are sampled from a simple prior, almost always a standard Gaussian:

z ~ N(0, I)      output = G(z)

This simulator uses a 3D latent space (real models use 100s–1000s of dimensions) so it can be watched directly. The scattered points are samples drawn from the Gaussian prior; the wireframe shell marks the ~3σ region where almost all mass lives. The morphing object is a toy decoder — each surface point's radius is a fixed function of the current latent vector z(t):

r(v, z) = 1 + 0.28·[ zx·sin(3vx + 2zy) + zy·sin(3vy + 2zz) + zz·sin(3vz + 2zx) ]
                 + σ·0.12·noise(v, time)

Because G is a smooth function, moving z smoothly between two sampled points A and B — latent interpolation — produces a smooth morph in output space, which is exactly why "walking the latent space" of a real GAN/VAE/diffusion model produces coherent in-between images instead of noise.

Linear vs Spherical — a straight line between two Gaussian samples dips through a lower-density region near the middle; spherical interpolation (slerp) keeps the path closer to the high-density shell, which is why it is the standard choice for VAE/GAN latent walks.
Temperature σ — adds stochastic noise to the decode, the same role "sampling temperature" or diffusion noise plays in real generators: σ = 0 gives a deterministic, faithful decode; higher σ trades fidelity for diversity/roughness.
Relative likelihood — shows exp(−‖z‖²/2), i.e. how probable this point is under the Gaussian prior relative to its peak at the origin. Points far from the cloud's center are rare samples and often decode to less coherent output in real models too.

Latent prior samples Point A Point B Decoded output G(z)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.