Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points (x0,x1)(mathbf{x}_0, mathbf{x}_1)(x0,x1) and ensuring that the velocity field is aligned, on average, with x1−x0mathbf{x}_1 – mathbf{x}_0x1−x0 when evaluated along a segment linking x0mathbf{x}_0x0 to x1mathbf{x}_1x1. While these pairs are sampled independently by default, they can also be selected more carefully by matching batches of nnn noise to nnn target… Read More
Flow Matching with Semidiscrete Couplings
Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points (x0,x1)(mathbf{x}_0, mathbf{x}_1)(x0,x1) and ensuring that the velocity field is aligned, on average, with x1−x0mathbf{x}_1 – mathbf{x}_0x1−x0 when evaluated along a segment linking x0mathbf{x}_0x0 to x1mathbf{x}_1x1. While these pairs are sampled independently by default, they can also be selected more carefully by matching batches of nnn noise to nnn target…
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