Wasserstein BaryBooster Turns Diffusion Realism into Event Forecasting Accuracy

Many models can predict what will happen to a bank customer, a patient, or an order over the next few steps. Almost nobody has tried to check whether those forecasts look like real life rather than just landing near the average. The authors of a new paper from Hugging Face Daily Papers close that gap. They built a benchmark for multi-step event sequence forecasting and showed that accuracy and distribution realism pull models in different directions. They then proposed Wasserstein BaryBooster, an algorithm that partially reconciles the two goals.

Why Event Sequences Are a Beast of Their Own

An event sequence is a chain of random events, each described by a set of heterogeneous features: numerical (payment amount, time between events) and categorical (transaction type, diagnosis, order status). Such data appears in finance, healthcare, business process analysis, and other fields. Classical time series forecasting methods handle it poorly, because the task is to predict not a single number but an entire trajectory of mixed types.

The authors frame the task as conditional generative modeling. The model receives a history and has to generate a plausible continuation several steps ahead. This framing also changes the evaluation criteria: it is not enough for a forecast to be close to the actual outcome. The set of generated trajectories must also look like real data.

A Benchmark Where Everyone Loses

The benchmark includes:

• metrics for two aspects of quality: forecast accuracy and distribution realism;
• strong statistical baselines;
• recent models adapted from adjacent fields;
• curated real-world datasets.

Careful evaluation produced an uncomfortable picture: no method delivers the best result in both directions at once. Models whose trajectories look the most natural lose on accuracy. Models that consistently land close to the actual outcome produce overly "smoothed" sequences that do not resemble real ones. The authors call this a fundamental tradeoff.

The reason is intuitive. To minimize error, it pays to predict something average. But the average of random events rarely matches what actually occurs in the data. A generative model, by contrast, faithfully reproduces the spread, and any single trajectory it produces can miss the mark.

BaryBooster:

Take Realism from Diffusion, Get Accuracy Through Aggregation

Against this backdrop, the authors introduce Wasserstein BaryBooster. The idea is to take a diffusion model with a strong realism score, generate a set of samples from it, and aggregate them into a single forecast. The name refers to the Wasserstein barycenter, a way of averaging distributions in the geometry of optimal transport. The aggregation accounts for the shape of the distribution rather than simply taking an arithmetic mean.

According to the authors, the resulting predictor reaches state-of-the-art accuracy. This shows that distribution realism can be converted into accuracy if the samples are combined into the final answer correctly. The tradeoff remains, but there is now a workable way to benefit from the generative component.

What Practitioners Should Do

The code for the benchmark and the algorithm is published on GitHub in the xaosina/event-sequence-forecasting repository. Teams that forecast transactions, customer journeys, clinical events, or business process steps should run their own models through the proposed metrics. If evaluation relies only on forecast error, you risk ending up with a model that quietly produces unrealistic trajectories. For simulations, stress tests, and synthetic data, that is critical.

The second practical takeaway concerns architecture. A diffusion model as a sample generator plus a separate aggregation layer makes it possible to tune the balance between realism and accuracy for the task at hand. For scoring, accuracy matters more; for scenario generation and simulation, realism does. For the first time, the benchmark makes it possible to measure both on the same data.