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Temporal dissipative solitons in nonlinear optical resonators are self-compressed, self-stabilizing and indefinitely circulating wave packets. Owing to these properties, they have been harnessed for the generation of ultrashort pulses and frequency combs in active and passive laser architectures, including mode-locked lasers1–4, passive fibre resonators5and microresonators6–11. Here, we demonstrate the formation of temporal dissipative solitons in a free-space enhancement cavity with a Kerr nonlinearity and a spectrally tailored finesse. By locking a 100-MHz-repetition-rate train of 350-fs, 1,035-nm pulses to this cavity-soliton state, we generate a 37-fs sech²-shaped pulse with a peak-power enhancement of 3,200, which exhibits low-frequency intensity-noise suppression. The power scalability unique to free-space cavities, the unprecedented combination of peak-power enhancement and temporal compression, and the cavity-soliton-specific noise filtering attest to the vast potential of this platform of optical solitons for applications including spatiotemporal filtering and compression of ultrashort pulses and cavity-enhanced nonlinear frequency conversion.