The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.
Compositional generalization requires models to produce novel configurations from familiar parts. In diffusion models, prior compositional generation methods typically assume that the relevant concepts or conditioning signals are already available. We instead ask whether a pretrained diffusion model can discover query-specific concepts from the time-indexed scores it learns for the noisy marginals pt(xt) and compose them at test time. Given a single out-of-distribution query, our method performs gradient ascent on sθ(xt,t)≈∇xtlogpt(xt) at multiple noising timesteps to recover local density modes, maps these modes into clean-space Gaussians, greedily selects relevant prototypes with a submodular likelihood objective, and combines them into a product-of-experts (PoE) teacher model with an analytic score. This teacher model can be sampled directly through classifier-free guidance or used to generate a sample pool for training a new class embedding and low-rank adapter. On held-out composition benchmarks built from ColorMNIST and CelebA, both the analytic PoE sampler and the low-rank adapted model outperform query-only and nearest trained-class baselines. These results suggest that the time-indexed score geometry of the diffusion model contains reusable density-mode concepts that support test-time compositional generation without a predefined concept library.
Diffusion models generate realistic visual content, yet often fail to produce rare but plausible compositions. When prompted with combinations that are valid but underrepresented in training data, such as a snowy beach or a rainbow at night, the generation process frequently collapses toward more common alternatives. We identify this failure mode as default completion bias, where denoising trajectories are implicitly attracted toward high-frequency semantic configurations. Existing guidance mechanisms do not explicitly model this competing tendency and therefore struggle to prevent such collapse. We introduce Default Completion Repulsion (DCR), a training-free framework that explicitly models and suppresses default completion behavior. DCR constructs a counterfactual attractor by relaxing the rare compositional factor while preserving surrounding semantics, inducing an alternative denoising trajectory reflecting the model's preferred completion. We define the discrepancy between target and attractor trajectories as a counterfactual drift, and propose a projection-based repulsion mechanism that removes guidance components aligned with this drift direction. This suppresses undesired frequent completions while preserving other semantic components. DCR operates entirely within the standard diffusion sampling process without retraining or architectural modification. Experiments on rare compositional prompts show that DCR improves compositional fidelity while maintaining visual quality. Our analysis further shows that the framework exposes and counteracts intrinsic model biases, offering a new perspective on controllable generation beyond explicit constraint enforcement.
Conditional generators provide a natural tool for controllable generation, including settings where the desired condition is a new composition of observed attributes or experimental factors. In many applications, especially in scientific domains, such models are attractive to explore conditions for which real samples are rare, expensive, or not yet observed. However, this creates a circularity for evaluation: standard conditional quality metrics require a reference target distribution, but in the extrapolative regime that distribution is unavailable by definition. We address this problem with a post-hoc, per-sample trust score for assessing conditional samples using only the training distribution. The score combines two estimable quantities: global realism, measuring compatibility with the real data manifold, and attribute-wise faithfulness, measuring whether a sample is closer to the requested attributes than to plausible alternatives. We show that the score can recover meaningful comparisons across extrapolated generations, under a mild coverage condition on the observed attributes. These comparisons enable effective filtering, ranking, and abstention of generations and can be used directly on off-the-shelf pretrained models. In biological imaging, selected samples preserve real morphological structure better and improve downstream predictive performance, while similar gains are observed on controlled vision benchmarks. Finally, we show how the score can be applied during generation, enabling abstention before full decoding. Code is available at https://github.com/berkerdemirel/faithful-cond-gen.
Berker Demirel, Valentino Maiorca, Marco Fumero +2