An optical downlink for the return of scientific data from space probes at interstellar distances is studied. The context is probes moving at relativistic speed using a terrestrial directed-energy beam for propulsion, necessitating very low mass probes. Achieving simultaneous communication from a swarm of probes launched at regular intervals to a target at the distance of Proxima Centauri is addressed. The analysis focuses on fundamental physical and statistical communication limitations on downlink performance rather than a concrete implementation. Transmission time/distance and probe mass are chosen to achieve the best data latency versus volume trade-off. Challenges in targeting multiple probe trajectories with a single receiver are addressed, including multiplexing, parallax, and target-star proper motion. Constraints on transmit aperture size make a compelling argument in favor of free-space optical communications, and this is the assumed approach for our baseline analysis. Relevant sources of background radiation, including cosmic, atmospheric, and receiver dark count, are identified and estimated. Direct detection enables high photon efficiency and incoherent aperture combining. A novel burst pulse-position modulation (BPPM) beneficially expands the optical bandwidth and ameliorates receiver dark counts. A canonical receive optical collector combines minimum transmit power with constrained swarm-probe coverage. Theoretical limits on reliable data recovery and sensitivity to the various BPPM model parameters are applied, including a wide range of total collector areas. Significant near-term technological obstacles are identified. Enabling innovations include a high peak-to-average power ratio, a large source extinguishing factor, the shortest atmosphere-transparent wavelength to minimize target-star interference, adaptive optics for atmospheric turbulence, very selective bandpass filtering (possibly with multiple passbands), very low dark count single-photon superconducting detectors, and very accurate attitude control and pointing mechanisms.