# CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates

arXiv: https://arxiv.org/abs/2507.17030 · HTML: https://mlsanity.com/paper/2507.17030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 15 of 15)

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- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
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- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Conditional diffusions for amortized neural posterior estimation](https://mlsanity.com/paper/2410.19105/) (2024)

## Abstract (arXiv)

We consider the problem of validating whether a neural posterior estimate ( q(θ mid x) ) is an accurate approximation to the true, unknown true posterior ( p(θ mid x) ). Existing methods for evaluating the quality of an NPE estimate are largely derived from classifier-based tests or divergence measures, but these suffer from several practical drawbacks. As an alternative, we introduce the Conditional Localization Test (CoLT), a principled method designed to detect discrepancies between ( p(θ mid x) ) and ( q(θ mid x) ) across the full range of conditioning inputs. Rather than relying on exhaustive comparisons or density estimation at every ( x ), CoLT learns a localization function that adaptively selects points θl(x) where the neural posterior q deviates most strongly from the true posterior p for that x. This approach is particularly advantageous in typical simulation-based inference settings, where only a single draw ( θ ~ p(θ mid x) ) from the true posterior is observed for each conditioning input, but where the neural posterior ( q(θ mid x) ) can be sampled an arbitrary number of times. Our theoretical results establish necessary and sufficient conditions for assessing distributional equality across all ( x ), offering both rigorous guarantees and practical scalability. Empirically, we demonstrate that CoLT not only performs better than existing methods at comparing p and q, but also pinpoints regions of significant divergence, providing actionable insights for model refinement. These properties position CoLT as a state-of-the-art solution for validating neural posterior estimates.