@drhead could you please explain this phenomenon?

Great question — this tripped me up initially too, but it makes sense once you think about it from a signal processing perspective.

The key insight is that min-SNR weighting is not about task difficulty — it's about gradient signal quality.

When t → 0 (low noise, high SNR), the model's prediction is already close to the clean signal. The loss gradients are small but stable and informative. When t → T (high noise, low SNR), the input is almost pure noise, so the model is essentially guessing — the gradients are large but extremely noisy and uninformative. They point in near-random directions.

Without min-SNR weighting, these noisy high-t gradients dominate training because their magnitude is large. This is analogous to a classical signal processing problem: a high-variance estimator with poor SNR can degrade overall system performance even if it carries some information. The optimal strategy (in a Wiener filter sense) is to attenuate components in proportion to their noise power.

That's exactly what min-SNR does: it clips the loss weight at high-noise timesteps to prevent those noisy gradients from overwhelming the useful signal from low/mid-noise timesteps.

Think of it this way:

• Without weighting: equal weight at all timesteps → high-noise timesteps dominate (large loss magnitude) → training is unstable
• With min-SNR: cap the contribution of high-noise timesteps → the model focuses on the regime where it can actually learn meaningful structure

The paper (Section 3.2) shows this formally: the optimal weighting under an SNR-based variance analysis is min(SNR(t), γ), which down-weights high-noise timesteps relative to the unweighted case. The γ parameter controls the clipping threshold — essentially your noise floor.

So it's not "easy tasks get high weight" — it's "timesteps where the gradient signal is reliable get preserved, noisy timesteps get attenuated." Classic matched filtering intuition applied to diffusion training.