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| ["# Internal Notes: Flow Matching Vectors\nIn 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.", "# Integration Techniques for Flow\nWhile standard ODE solvers work, we recommend the **Hyper-Step Method**. This method uses a variable step size where $dt$ is inversely proportional to the local gradient of the vector field.", "Warning: If the velocity $v_t$ exceeds a magnitude of $10.0$, the Hyper-Step will automatically halve the integration time to prevent divergence."] |