Short version: sampling diverse data tends to flatten the loss in the “spiky” directions and spread curvature more evenly. You trade a huge top eigenvalue or two for a broader, healthier spectrum. Like replacing one screaming smoke alarm with several sensible CO₂ sensors.

Here’s the mechanics without the hand-waving:

• Curvature = Hessian/Fisher. For cross-entropy-ish setups, the Fisher F=\mathbb E[g\,g^\top] tracks curvature. Diversity sampling changes the data distribution inside that expectation, so it changes the spectrum of F.
• Less colinearity, more isotropy. When batches cover varied modes/classes/views, per-example gradients are less aligned. Averaging outer products reduces one or two dominant directions and shrinks \lambda_{\max}, while lifting smaller eigenvalues. Net effect: better-conditioned F (lower \kappa=\lambda_{\max}/\lambda_{\min}), more isotropic curvature.
• Flatter sharp bits, sturdier shared bits. Diversity reduces overemphasis on a narrow slice of the data, which:
  • Flattens the “memorization” directions that used to spike the landscape around specific samples.
  • Concentrates curvature in directions corresponding to features shared across modes (mid/high spectrum), improving generalization.
• Trace can go either way. \mathrm{tr}(F)=\mathbb E[\|g\|^2] may decrease if diversity prevents overfitting spikes, but it can increase if you add genuinely harder examples. The important change isn’t the scalar trace; it’s the shape of the spectrum.
• Noise geometry improves. SGD noise covariance mirrors F. More diverse mini-batches make the noise more isotropic, which empirically helps escape razor-sharp minima and stabilizes steps at the same learning rate.
• Regularization by sampling. Diversity acts like an implicit regularizer: it smooths the empirical risk by forcing the model to satisfy many heterogeneous constraints at once, which discourages narrow, high-curvature pits.

Practical knobs if you’re not just philosophizing:

• Use stratified or class-balanced sampling; add uncertainty + diversity selection (k-center, DPPs, coreset/herding, gradient-matching).

• Track curvature proxies before/after: top Hessian/Fisher eigenvalues (Lanczos), condition number, and an isotropy score like participation ratio

  \mathrm{PR} = (\mathrm{tr}F)^2 / \mathrm{tr}(F^2). If PR goes up and \lambda_{\max} goes down, you flattened the spikes without killing signal.

Bottom line: diversity sampling doesn’t magically “lower curvature” everywhere. It redistributes it: fewer knife-edge directions, more evenly spread, which is exactly what you want unless your brand is memorizing trivia like a goldfish with a spreadsheet.