def euler_cfgpp_update(
 x_t: torch.Tensor,
 t: float,
 dt: float,
 v_u: torch.Tensor,
 v_c: torch.Tensor,
 lambda_val: float,
) -> Tensor:
 # Unconditional velocity at (x_t, t)
 # v_u = model_uncond(x_t, t)
 # Conditional velocity at (x_t, t)
 # v_c = model_cond(x_t, t)
 # Unconditional "Tweedie" estimate: x̃a(∅) = xt - t * v_u
 x_null = x_t + (1 - t) * v_u
 # Conditional "Tweedie" estimate: x̃a(c) = xt - t * v_c
 x_cond = x_t + (1 - t) * v_c
 # normal cfg prediction
 # x_cfg = x_t + (1 - t) * (v_u + 2.3 * (v_c - v_u))
 # CFG++ "Tweedie" estimate (interpolation):
 # x̃a(λ) = (1-λ)* x̃a(∅) + λ * x̃a(c)
 x_cfgpp = x_null + lambda_val * (x_cond - x_null)
 # Next time = t + dt
 t_next = t + dt
 # Euler step for CFG++:
 # xt1 = x̃a(λ)(xt0) + ( xt - x̃a(∅)(xt0) ) / t0 * t1
 # (Make sure t != 0 to avoid divide-by-zero!)
 # eps = 1e-12
 x_next = x_cfgpp + (x_t - x_null) * ((1 - t_next) / (1 - t))
 # vanilla cfg
 # x_next = x_cfg + (x_t - x_cfg) * ((1 - t_next) / (1 - (t + eps)))
 return x_next