Understanding when language diffusion models memorize training data versus generalize remains an open challenge. We address it by framing Uniform-based Discrete Diffusion Models (UDDMs) as Associative Memories (AMs) where **both memorization and creativity coexist**. Unlike Hopfield networks, which require an energy function to produce attractors, we show that attractors can be formed via conditional likelihood maximization. We observe that UDDMs treat both training and unseen test sequences as fixed points for denoising while retaining the capacity to synthesize novel texts. We demonstrate that, as training set size increases, attractor basins around training samples shrink while those around unseen test samples expand until they become indistinguishable. This transition can be detected via the conditional entropy of tokens, which vanishes during memorization. Our framework provides both a theoretical foundation and a practical metric to elucidate the generative regimes of UDDMs.