The black-box route differentiates Q through all F denoise steps — so the gradient is a product of F Jacobian matrices, J_F-1·…·J₀. Watch the cost in 3-D: a unit gradient sphere at x^F is carried back along the chain, and every step's Jacobian stretches and rotates it. It doesn't merely grow like λ^F — it turns into a long, thin, twisted ellipsoid (the condition number blows up), so the gradient direction becomes dominated by one stretched axis and is numerically fragile. Crank F and λ, hit backprop, and orbit the camera. This whole mess is what RQL's one-hop-per-step update avoids.