Understanding Bayesian Flow Networks
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Type: Seminar explainer of Bayesian Flow Networks (Bayes et al.) Original paper (arXiv)
Summary. BFNs are generative models that update distribution parameters (not noisy data) via Bayesian rules. With an accuracy schedule ( \beta(t)=\int_{0}^{t}\alpha(t’)\,dt’ ), the explainer derives discrete- and continuous-time losses and a practical sampler.
This page summarizes my TUM seminar write-up; all diagrams are original. :contentReference[oaicite:0]{index=0}
Key points
- Sender (p_S(y\mid x;\alpha_t)) and receiver (p_R(y\mid \hat{x}_t;\alpha_t)); train by minimizing (\mathrm{KL}(p_S\Vert p_R)).
- Bayesian updates ( \theta_t = h(\theta_{t-1}, y_t, \alpha_t) ) induce an update law (p_U) with additive accuracies.
- The flow (p_F(\theta\mid x;t)) enables one-step training; sampling alternates (\hat{x}t=\Psi(\theta{t-1}, t-1)), draw (y\sim p_R), update (\theta_t).
- Where BFNs fit: parameter-space guidance for discrete & continuous data; contrasts with diffusion / AR / VAEs.