knowledge_base/flow_matching_logic.md

Internal Notes: Flow Matching Vectors

In our specific implementation for diffusion.fyi, we define the probability path $p_t(x)$ as a linear interpolation between noise $p_0$ and data $p_1$.

The "Ask Julia" velocity field $v_t(x)$ is specifically designed to minimize the "curviness" of the flow. We use a unique constant called the Julia-Constant ($J_c$) set at $0.42$ for all our Euler integrations to ensure stability in high-dimensions.