Learning Transverse Momentum Distributions from Raw Scattering Events via Conditional Diffusion
Authors: Jitao Xu, Christopher Cocuzza, Kevin Braga, Daniel Lersch, Nobuo Sato, Yaohang Li
Organizations: Department of Computer Science, Old Dominion University · Department of Physics, William & Mary · Thomas Jefferson National Accelerator Facility
Extracting transverse momentum dependent parton distribution functions (TMD PDFs) from semi-inclusive deep inelastic scattering (SIDIS) data is a central goal of the nucleon structure program at Jefferson Lab and the future Electron-Ion Collider. Traditional extraction methods rely on parameterized functional forms and iterative fitting, which can limit the flexibility of the resulting distributions and make uncertainty quantification cumbersome. We present a conditional diffusion model that learns to map raw SIDIS event kinematics directly to TMD PDFs, bypassing explicit functional assumptions. Evaluated on simulated SIDIS data at CLAS12 kinematics, the model recovers the underlying TMD with informative uncertainties that narrow steadily with increasing event statistics, and produces reliable estimates even with as few as 1,000 conditioning events, a statistics-limited regime directly relevant to ongoing and planned experiments.
Figures & tables
Figure 1: Overview of the proposed framework. A variable-size set of raw SIDIS events is first mapped to per-point features by a shared PointNet convolution layer, then aggregated through six-way global pooling and refined by a lightweight Transformer encoder to produce a fixed-dimensional conditioning vector. This vector, together with a sinusoidal timestep embedding, guides a 2D UNet that iteratively denoises Gaussian noise into a predicted TMD image f(x,bT) .
Figure 2: Evolved TMD f(x,Q2,bT) on the full (x,bT) grid at a representative Q2 slice. (a) Theory ground truth. (b–d) Diffusion model predictions (ensemble mean over 128 noise replicas) conditioned on Nev=1,000 , 10,000 , and 100,000 events, respectively.
Figure 3: This figure shows one-dimensional slices of the two-dimensional TMD in Figure 2 , at fixed x as a function of bT . Evolved TMD slices at epoch 1,000 for three conditioning event counts. Dark gray: theory ground truth. Blue line and band: diffusion model mean ±3σ over 128 noise replicas. Bottom panels: absolute model standard deviation σ . As Nev increases, the prediction converges to the true TMD with narrowing uncertainty.