The practical capabilities of contemporary quantum processors are largely limited by noise. Eventually, this problem will be resolved using quantum error correction, but in the meantime we can improve performance using error-mitigation techniques. Probabilistic error cancellation (PEC) is one such technique and works by forming a model of the noise associated with one or more gates in a quantum circuit. By generating circuit instances with samples from the inverse noise distribution, we can effectively cancel the noise on such gates and improve the accuracy of measured observables. One major challenge for PEC has been to find a noise model that is scalable in the number of qubits, that can capture correlated noise and that can be efficiently learned and manipulated. In this talk we present a Pauli-Lindblad noise model that simultaneously satisfies all these criteria. For common qubit topologies, the number of parameters scales linearly with the number of qubits, and learning is efficiently done using a combination of cycle benchmarking and nonnegative least-squares fitting. The special structure of the noise model results in a particularly simple algorithm for sampling from the inverse. Combined, this allows us to learn and mitigate noise on layers of concurrent CNot gates, and demonstrate the power of PEC on problem sizes there were previously far beyond reach.