Sander Dieleman on typicality: why likelihood fails for perceptual generative models
sedielem · x · 2026-10-21
Responding to a question, DeepMind researcher Sander Dieleman points to his 2020 essay Musings on Typicality, adding that input-space likelihood is usually not what you want for perceptual signals—you can reweight it (as diffusion models do) or measure it in a different representation space.
Key points from the essay:
- Typicality: in high dimensions, samples almost always fall in a "typical set" whose typical negative log-likelihood far exceeds the entropy—explaining why high-dimensional Gaussians behave like "soap bubbles."
- Why beam search fails for autoregressive image/audio/video models: the search favors atypical, weird samples with misleadingly high likelihood.
- Why thresholding likelihood doesn't work for anomaly detection with generative models.
- The right level of abstraction: measure probability in a suitable representation space, not raw inputs.
A foundational read for understanding generative models' counterintuitive high-dimensional behavior.
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