Improve score and flow matching

[manuelgloeckler]

🚀 Feature Request

Is your request related to a problem?

Following the recent hackathon, we implemented basic infrastructure for score and flow matching, but currently, their performance lags behind (issue #1374). One major issue is suboptimal default parameter settings and improper training approaches. Additionally, some features are lacking (issue #1226). Despite similarities, flow and score matching remain disconnected.

Describe the solution you'd like

To address these issues, improvements in performance and feature sets are crucial.

📌 Additional Context

There are several related tasks; if you identify others, please add them. For context:

• Better NN architectures #1442 requires knowledge of diffusion models and suitable architectures.
• Unify Flow and Score matching to some degree #1440 necessitates understanding of SBI internals and benefits from experienced contributors.
• Add new diffusion samplers #1438 involves diffusion models and SDE solvers, but is somewhat self-contained.
• Add explicit training/evaluation noise schedules #1437 is well-documented but benefits from familiarity with diffusion models.
• Extend ScoreEstimator training approaches #1436 does need quite some knowledge on diffusion models and might needs some internal restructurings.
• Better training loop for diffusion models and flow matching #1445 is somewhat related to Extend ScoreEstimator training approaches #1436 but with regard to what default optimizer schedules and more one should use
• Add API for guidance #1446 needs some background knowledge on guidance, but is fairly independent from the other issues.