Irregularly sampled multivariate event streams remain a difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude. We (i) propose \textbf{SurF}, a generative model that uses the Time Rescaling Theorem (TRT) as a learnable bijection between event sequences and i.i.d.\ unit-rate exponential noise, enabling a single model to be trained across heterogeneous event-stream datasets; (ii) three efficient parameterizations of the cumulative intensity that scale to long sequences; and (iii) a Transformer-based encoder for multi-dataset pretraining. On six real-world benchmarks, SurF achieves the best reported time RMSE on Earthquake, Retweet, and Taobao, and is within trial-level noise of the strongest specialist on the remaining three. Under a strict leave-one-out protocol, the held-out checkpoint beats every classical and neural-autoregressive baseline on $5/6$ datasets and beats every baseline on Amazon and Earthquake, an initial step toward foundation models over asynchronous event streams (Code is available at https://github.com/MrRezaeiUofT/SurF).

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