Artificial intelligence increasingly guides decisions in safety-critical settings, yet neural networks can remain overconfident when confronted with ambiguous observations or unfamiliar inputs. Bayesian neural networks quantify such uncertainty by replacing every weight with a probability distribution, but sampling many distributions at prediction time overwhelms deterministic digital hardware. Here we show that the temporal speckle of broadband light provides a native physical representation of probabilistic weights. Random beating among the frequency components of individually amplitude-bandwidth programmed spectral channels enables optical-encoding of mean and variance in each channel independently. This way, a single broadband light source stores many probabilistic weights in parallel and delivers mutually uncorrelated samples without requiring computationally demanding random-number generation. We harness this mechanism in an ultrafast photonic processor that computes one probabilistic convolution every 37.5 ps and allows simultaneous classification and out-of-distribution detection in hybrid Bayesian neural networks. Our system classifies blood-cell images while recognizing withheld cell types as unfamiliar, and separates epistemic novelty from aleatoric ambiguity on standard uncertainty benchmarks. Programming probability distributions into the fluctuations of light removes the sampling bottleneck of Bayesian inference and opens a route to high-speed, uncertainty-aware photonic AI.

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