Concentration phenomenon in quantum generative learning and mitigation via truncated QuDDPM

Quantum generative learning aims to generate quantum states from an ensemble with samples. The Quantum Denoising Diffusion Probabilistic Model (QuDDPM) employs parameterized quantum circuits and mid-circuit measurements to transport an initial random-state ensemble to the target ensemble, demonstrating promising capability in generative learning tasks; however, its mechanism and limitations are not well understood. In this work, we analytically show that for typical Haar random unitaries, the state ensemble conditioned on any fixed measurement trajectory concentrates toward a single state regardless of input states, and we confirm with numerical simulations. To avoid this concentration and leverage input randomness, we propose a truncated QuDDPM that terminates the forward diffusion at an intermediate step and generates new quantum data from partially scrambled states. The truncated QuDDPM reduces the number of steps and mitigates the trainability issue induced by random inputs. Our results provide a theoretical interpretation of ensemble transport in diffusion-based quantum models and a strategy to improve QuDDPM's performance.