# Mode Collapse Is Cheap to Detect: A Ground-Truth-Free Pre-Flight Check for Neural Samplers

arXiv: https://arxiv.org/abs/2609.26272 · HTML: https://mlsanity.com/paper/2609.26272/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 30 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Beyond ELBOs: A Large-Scale Evaluation of Variational Methods for Sampling](https://mlsanity.com/paper/2406.07423/) (2024)
- [Sequential Controlled Langevin Diffusions](https://mlsanity.com/paper/2412.07081/) (2024)
- [Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics](https://mlsanity.com/paper/2502.08696/) (2025)
- [No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers](https://mlsanity.com/paper/2502.06685/) (2025)
- [Proximal Diffusion Neural Sampler](https://mlsanity.com/paper/2510.03824/) (2025)
- [Progressive Tempering Sampler with Diffusion](https://mlsanity.com/paper/2506.05231/) (2025)
- [On scalable and efficient training of diffusion samplers](https://mlsanity.com/paper/2505.19552/) (2025)
- [Batch, match, and patch: low-rank approximations for score-based variational inference](https://mlsanity.com/paper/2410.22292/) (2024)
- [Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processes](https://mlsanity.com/paper/2605.03984/) (2026)
- [End-To-End Learning of Gaussian Mixture Priors for Diffusion Sampler](https://mlsanity.com/paper/2503.00524/) (2025)
- [Diffusion Bridge Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/2509.19078/) (2025)
- [Model-Informed Flows for Bayesian Inference](https://mlsanity.com/paper/2505.24243/) (2025)
- [Diffusion models recover accurate mixture weights despite score function insensitivity](https://mlsanity.com/paper/2607.15485/) (2026)
- [Denoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriors](https://mlsanity.com/paper/2401.02739/) (2024)
- [FlowVAT: Normalizing Flow Variational Inference with Affine-Invariant Tempering](https://mlsanity.com/paper/2505.10466/) (2025)
- [Fisher meets Feynman: score-based variational inference with a product of experts](https://mlsanity.com/paper/2510.21598/) (2025)
- [Normalizing Flow Regression for Bayesian Inference with Offline Likelihood Evaluations](https://mlsanity.com/paper/2504.11554/) (2025)
- [Large-scale Score-based Variational Posterior Inference for Bayesian Deep Neural Networks](https://mlsanity.com/paper/2602.05873/) (2026)
- [Conditional Diffusion Sampling](https://mlsanity.com/paper/2605.04013/) (2026)

## Abstract (arXiv)

Neural samplers are trained against an unnormalised target tildeπ=e-E with no samples from π, which leaves the practitioner with no way to tell whether an expensive training run has silently dropped part of the target. The diagnostics in common use are computed from the model's own draws and are therefore confined to the model's support: we exhibit a sampler whose self-normalised effective sample size is 0.99 while it misses 87% of the target mass. We argue that detecting missing mass is a strictly easier problem than sampling it: detection needs one point per missed basin plus a local curvature estimate, whereas correction needs the sampler retrained. We turn this into a pre-flight check that consumes a few percent of the sampler's own training budget and uses only E, nabla E and nabla2 E. On Gaussian-mixture, Many-Well and rotated anisotropic Many-Well targets with exactly computable ground truth, the check estimates the missing mass to within 10-3 at 2.7% of training cost, where a tuned annealed SMC reference needs 70--280% of training cost to do worse. It also applies unchanged to a controlled-SDE sampler that has no tractable density, where ESS and the ELBO cannot be formed at all. The estimator carries a self-diagnostic that, without ground truth, is conservative in the safe direction: across 60 configurations it clears 16, of which 15 are accurate to 10-2 or better. We are explicit about what this does and does not license: the check cheaply produces evidence of missing mass, and sometimes evidence that the search has stabilised, but it cannot certify a run, and its thresholds are heuristic. We then map the boundary of the method on a real physical landscape, LJ-13, and report where it fails and why.