Research map / Probabilistic and scientific modeling / Variational and generative sampling

Multiobjective distribution matching

ICML 2025 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Flow matching and flow sampling

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Develops information-geometry theory giving closed-form Pareto sets and fronts for multiobjective distribution matching over exponential families under KL/inverse KL (and alpha) divergences, and applies it to a multiobjective VAE for interpolating image distributions.

Problem

Generating a single distribution that simultaneously matches multiple (possibly conflicting) target distributions, i.e., finding the Pareto set and front of multiobjective distribution matching.

Approach

Uses dually flat manifold structure of exponential families so that the Pareto set under KL and inverse KL is the convex hull of the target distributions in natural or expectation coordinates, giving explicit closed forms for MVNs and an alpha-divergence Pareto set; these are used to interpolate latent MVNs in a multiobjective VAE.

Key results

• Derives closed-form Pareto set for MVN distributions under KL divergence (mean and precision-weighted linear combinations) and shows gradient descent solutions match the theoretical Pareto front in a 3-dimensional example.
• Shows the Pareto set under alpha-divergence is a normalized mixture of powered densities, with KL and reverse KL as special cases.
• MOVAE with a single model generates smooth interpolations between alarm-clock and circle image distributions on QuickDraw across preference vectors.

Limitations

• Paper focuses on theory and does not deeply explore applications.
• Experiments are small-scale (28x28 QuickDraw images, qualitative results only).
• Future directions (LLMs, trustworthy ML) are not explored.

Experimental setup

Datasets: QuickDraw

Benchmarks: QuickDraw

Metrics: Pareto front (KL divergence values) qualitative interpolation quality

Baselines: gradient descent solutions VAE mixture models

Builds on: Tchebycheff scalarization Pareto set learning variational autoencoder Bregman divergence

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