We present TabPFN, an AutoML method that is competitive with the state of the art on small tabular datasets while being over 1,000$\times$ faster. Our method is very simple: it is fully entailed in the weights of a single neural network, and a single forward pass directly yields predictions for a new dataset. Our AutoML method is meta-learned using the Transformer-based Prior-Data Fitted Network (PFN) architecture and approximates Bayesian inference with a prior that is based on assumptions of simplicity and causal structures. The prior contains a large space of structural causal models and Bayesian neural networks with a bias for small architectures and thus low complexity. Furthermore, we extend the PFN approach to differentiably calibrate the prior's hyperparameters on real data. By doing so, we separate our abstract prior assumptions from their heuristic calibration on real data. Afterwards, the calibrated hyperparameters are fixed and TabPFN can be applied to any new tabular dataset at the push of a button. Finally, on 30 datasets from the OpenML-CC18 suite we show that our method outperforms boosted trees and performs on par with complex state-of-the-art AutoML systems with predictions produced in less than a second. We provide all our code and our final trained TabPFN in the supplementary materials.