"""MeanFlow 损失（Geng et al. 2025；MP1 配方：25% 样本 r≠t，自适应损失加权）。
约定：t=0 为数据、t=1 为噪声；z_t = (1−t)·x + t·ε，瞬时速度 v = ε − x；网络输出平均速度 u(z,r,t)。
目标 u_tgt = v − (t − r)·du/dt，du/dt = v·∂_z u + ∂_t u 用 torch.func.jvp 一次前向得到（切向量 (v, 0, 1)）。"""
import torch
from torch.func import jvp


def sample_rt(B, device, dtype, p_neq=0.25, mu=-0.4, sigma=1.0):
    t = torch.sigmoid(torch.randn(B, device=device, dtype=dtype) * sigma + mu)
    r = torch.sigmoid(torch.randn(B, device=device, dtype=dtype) * sigma + mu)
    t, r = torch.maximum(t, r), torch.minimum(t, r)
    eq = torch.rand(B, device=device) >= p_neq
    r = torch.where(eq, t, r)
    return r, t


def meanflow_loss(model, mem, x, p_neq=0.25, ada_p=1.0, ada_c=1e-3):
    B = x.shape[0]
    r, t = sample_rt(B, x.device, x.dtype, p_neq)
    e = torch.randn_like(x)
    z = (1 - t)[:, None, None] * x + t[:, None, None] * e
    v = e - x
    fn = lambda z_, r_, t_: model.decode(mem, z_, r_, t_)
    u, dudt = jvp(fn, (z, r, t), (v, torch.zeros_like(r), torch.ones_like(t)))
    u_tgt = (v - (t - r)[:, None, None] * dudt).detach()
    err = (u - u_tgt).pow(2).mean(dim=(1, 2))
    w = 1.0 / (err.detach() + ada_c).pow(ada_p)
    return (w * err).mean(), err.mean().detach()


def one_step(model, mem, e):
    B = e.shape[0]
    one = torch.ones(B, device=e.device, dtype=e.dtype)
    return e - model.decode(mem, e, torch.zeros_like(one), one)