Improving generative model-based unfolding with Schrödinger bridges

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area; one based on discriminative models and one based on generative models. The main advantage of discriminative models is that they learn a small correction to a starting simulation while generative models scale better to regions of phase space with little data. We propose to use Schrödinger bridges and diffusion models to create sbunfold, an unfolding approach that combines the strengths of both discriminative and generative models. The key feature of sbunfold is that its generative model maps one set of events into another without having to go through a known probability density as is the case for normalizing flows and standard diffusion models. We show that sbunfold achieves excellent performance compared to state of the art methods on a synthetic $Z+\text{jets}$ dataset.

Figure 1

Comparison between different unfolding algorithms for six different physics observables unfolded. All observables are unfolded simultaneously without binning, with histograms shown only for evaluation. Results are evaluated over 600,000 pseudodata points. Statistical uncertainties are shown only in the ratio panel. Pseudodata and simulation are described by pythia.

Figure 2

Pairwise correlation plot between all unfolded variables using the cinn (left) or sbunfold (right) algorithms compared to the expected distributions from pythia events (truth).

Figure 3

Comparison between different unfolding algorithms for six different physics observables unfolded. All observables are unfolded simultaneously without binning, with histograms shown only for evaluation. Results are evaluated over 600,000 pseudodata points. Statistical uncertainties are shown only in the ratio panel. Pseudodata is taken from Herwig while pythia is taken as the main simulator.

Figure 4

Comparison between different unfolding algorithms for six different physics observables unfolded. All observables are unfolded simultaneously without binning, with histograms shown only for evaluation. Results are evaluated over 1,000 pseudodata points, the same number was used to train omnifold while other algorithms only rely on simulation. Statistical uncertainties are shown only in the ratio panel. Pseudodata is taken from Herwig while pythia is taken as the main simulator.

Figure 5

Comparison between different unfolding algorithms for six different physics observables unfolded. Results are evaluated over 600,000 pseudodata points. Statistical uncertainties are shown only in the ratio panel. Pseudodata and simulation are described by pythia.

Figure 6

Migration distribution between reconstructed level events and generator level distribution after unfolding with sbunfold. Results are evaluated over 600,000 pseudodata points. Pseudodata is taken from Herwig while pythia is taken as the main simulator.