Zero-noise conditional-mean anchor

Integrate the method at the generator input and training-loss level. Let context contain the past frames or tokens, target be the next frame, and z be the Gaussian noise supplied to the existing conditional generator, diffusion denoiser, flow model, or FGN. For every minibatch, sample the usual z ~ Normal(0,I) and compute the original generative loss L_gen = generative_loss(model(context,z), target, z). Create a zero tensor z0 with the same shape as z, compute mean_pred = model(context,z0), and add L_mpr = mean((mean_pred-target)^2) over output dimensions. Backpropagate L_total = L_gen + lambda * L_mpr, initially sweeping lambda over {0.01, 0.1, 1.0} after normalizing both losses by the number of output elements. If the architecture has a diffusion timestep or noise-level input in addition to latent noise, apply the anchor to the final clean-state prediction or predicted residual associated with zero latent conditioning while retaining the normal diffusion timestep schedule. At inference, use z0 for a deterministic mean forecast and nonzero Gaussian seeds for stochastic samples. The paper supplies the zero-noise anchor and squared-error objective; estimate lambda, loss normalization, and whether to stop gradients through any auxiliary branch empirically. First test a small conditional video or PDE-style rollout benchmark with a 2D UNet or transformer over 5-10 prediction steps. Compare the baseline and MPR models at equal optimizer steps and report one-step MSE, 20-step rollout error, ensemble variance, and calibration or CRPS. Success is lower long-horizon error and reduced deterministic-rollout variance without collapse of stochastic diversity or a substantial increase in training FLOPs.