Moving Beyond the DRW Model: Learning Quasar Variability with Generative Models

The optical continuum variability of quasars is often described by a damped random walk (DRW) model, with characteristic damping timescales $τ_{\rm DRW}$ of hundreds of days and amplitudes $σ_{\rm DRW}$ of $\mathcal{O}(0.1)$ magnitudes. This model has been widely used as a null hypothesis to assess the significance of periodic signals in quasar light curves in the search for supermassive black hole binaries, the significance of extreme quasar variability like tidal disruption events (TDEs) and changing-look (CL) quasars, or to model time lags in reverberation mapping. However, the DRW model is known to be incomplete, and an incorrect null hypothesis can lead to biased significance estimates. We investigate the impact of such null-hypothesis mis-specification on the detection of periodic signals in synthetic quasar light curves and introduce the generative model Nullasar, capable of learning quasar variability directly from time-series data. We demonstrate that Nullasar, trained with flow matching, can learn delicate statistical properties of stochastic light-curve variability without explicitly assuming any noise model. We further demonstrate that Nullasar can learn correlated distributions of noise parameters and generate new light-curve realizations from a range of deviations from the Gaussian DRW noise model, approximating parametric descriptions of stochastic processes. When used as a null hypothesis for detecting periodic signals in synthetic light curves, Nullasar performs comparably to fitting the correct DRW model to each light curve, and outperforms parametric fitting when the variability follows a more flexible AR(2) model. Finally, we identify practical limitations, including sensitivity to contamination of the training set by non-null signals, and show that projecting the conditioning vector of the model onto its leading principal components largely mitigates it.