Spectral Signatures of Memorization Basins in Diffusion Trajectories

Achref Jaziri, Martin Mundt, Ahmed Imtiaz Humayun, Visvanthan Ramesh

Diffusion models are known to reproduce individual examples from their training data as a form of memorization with implications for generalization, privacy, and downstream use. Recent work demonstrated that memorized training samples reside inside contiguous regions of the data/latent space known as basins of memorization -- once a denoising trajectory enters a basin, under finite perturbations it irreversibly reproduces a memorized example. Prior empirical work on such basins in trained models has primarily focused on classifier-free guidance based detection and mitigation strategies in text-to-image models, leaving basin entry and their formation largely uncharacterized. In this paper, we present a geometric characterization of memorization basins for conditional, unconditional, and rectified-flow-based diffusion models. We observe a characteristic signature in the local spectrum of the function geometry that distinguishes basin entry: the emergence of a dominant singular mode followed by a sharp spectral recovery. This signature appears at two timescales: along denoising trajectories during inference and over the course of training. We further investigate whether these…