Large-scale diffusion models have demonstrated remarkable success across a variety of domains. These models not only exhibit exceptional performance in their primary tasks but also adapt well to downstream applications through the 'pre-train & fine-tune paradigm'. However, the potential misuse of diffusion models for generating unsafe content has raised significant concerns regarding their governance and regulation, necessitating robust unsafe output prevention strategies. Despite the urgent demand for mitigation techniques, a significant challenge persists: once a model is distributed for local deployment or fine-tuning, the model provider and third-party regulators relinquish control over the model's behavior.

To aggregate useful information among diversified sources, a hotspot research topic called truth discovery has emerged in recent years. Existing truth discovery methods attempt to infer the true attribute values for the entities by identifying and trusting reliable data sources. That is, the values provided by reliable sources are more likely to be the true values. However, all these methods neglect the relations among different entities, which play important roles in truth discovery task. When reliable data sources cannot provide sufficient information of entities, the true attribute values of these entities can still be inferred by propagating trustworthy information from related entities. Motivated by this, in this paper, we introduce theconstrained truth discoveryproblem. We incorporate denial constraints, a universally quantified first-order logic formalism which can express a large number of effective and widely existing relations among entities, into the process of truth discovery. We formulate it as a constrained optimization problem and analyze its hardness. To address the problem, we propose algorithms to partition the entities into disjoint groups, and generate arithmetic constraints for each disjoint group separately. Then, the true attribute values of the entities in each disjoint group are derived by minimizing the objective function under the corresponding arithmetic constraints. Experimental results on both real-world and synthetic datasets demonstrate that the proposed approach achieves good performance even with very few constraints and reliable sources.

Aggregating the information provided by multiple data sources, which is also known as information integration , plays an important role in data analytics. Since there often exists recording errors, intentional errors, conflicts and outdated data across different data sources, finding the true attribute values of each entity is a fundamental task of crucial importance [3] . The process to fulfill this task is called truth discovery , which has been extensively studied in the literature.