import torch


def flow_match_xt(x0: torch.Tensor, n: torch.Tensor, t: torch.Tensor) -> torch.Tensor:
    r"""Forward process of flow matching."""
    return (1.0 - t) * x0 + t * n


def flow_match_target(n: torch.Tensor, x0: torch.Tensor) -> torch.Tensor:
    r"""Loss target for flow matching."""
    return n - x0