Fangjun Hu

Yifan F. Zhang, Fangjun Hu, Guangkuo Liu et al.

Diffusion models undergo a phase transition in a critical time window during generation dynamics, with two complementary diagnoses of criticality. The symmetry breaking picture views the critical window as when trajectories bifurcate into different semantic minima of the energy landscape, whereas the nonlocality picture views the critical window as when local denoising fails. We study whether two notions of such phase transitions are concurrent in modern diffusion transformers. By evaluating the dynamics and outcomes of the generation trajectory, we observe a near-simultaneous occurrence of the non-locality and symmetry breaking critical times. Our work is the first to unify the two notions of phase transitions in practice: it provides a concrete diagnostic for when and why diffusion models rely on conditioning and global denoising, enabling principled evaluation of model efficiency and guiding the design of architectures and sampling schemes that avoid unnecessary computation.

Fangjun Hu, Christian Kokail, Milan Kornjača et al.

Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by recent developments in mixed state phases of matter, we focus on arbitrary states in the trivial phase. A state belongs to the trivial phase if there exists a shallow preparation channel circuit under which local reversibility is preserved throughout the preparation. We prove that any mixed state in this class can be efficiently learned from measurement access alone. Specifically, given copies of an unknown trivial phase mixed state, our algorithm outputs a shallow local channel circuit that approximately generates this state in trace distance. The sample complexity and runtime are polynomial (or quasi-polynomial) in the number of qubits, assuming constant (or polylogarithmic) circuit depth and gate locality. Importantly, the learner is not given the original preparation circuit and relies only on its existence. Our results provide a structural foundation for quantum generative models based on shallow channel circuits. In the classical limit, our framework also inspires an efficient algorithm for classical diffusion models using only a polynomial overhead of training and generation.

Fangjun Hu, Guangkuo Liu, Yifan Zhang et al.

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided by score functions. Real-life data, like images, is often spatially structured in low-dimensional spaces. However, ordinary diffusion models ignore this local structure and learn spatially global score functions, which are often computationally expensive. In this work, we introduce a new perspective on the phases of data distributions, which provides insight into constructing local denoisers with reduced computational costs. We define two distributions as belonging to the same data distribution phase if they can be mutually connected via spatially local operations such as local denoisers. Then, we show that the reverse denoising process consists of an early trivial phase and a late data phase, sandwiching a rapid phase transition where local denoisers must fail. To diagnose such phase transitions, we prove an information-theoretic bound on the fidelity of local denoisers based on conditional mutual information, and conduct numerical experiments in a real-world dataset. This work suggests simpler and more efficient architectures of diffusion models: far from the phase transition point, we can use small local neural networks to compute the score function; global neural networks are only necessary around the narrow time interval of phase transitions. This result also opens up new directions for studying phases of data distributions, the broader science of generative artificial intelligence, and guiding the design of neural networks inspired by physics concepts.