Data unlearning aims to remove the influence of specific training samples from a trained model without requiring full retraining. Unlike concept unlearning, data unlearning in diffusion models remains underexplored and often suffers from quality degradation or incomplete forgetting. To address this, we first observe that most existing methods attempt to unlearn the samples at all diffusion time steps equally, leading to poor-quality generation. We argue that forgetting occurs disproportionately across time and frequency, depending on the model and scenarios. By selectively focusing on specific time-frequency ranges during training, we achieve samples with higher aesthetic quality and lower noise. Finally, to evaluate both deletion and quality of unlearned data samples, we propose a simple normalized version of SSCD. Together, our analysis and methods establish a clearer understanding of the unique challenges in data unlearning for diffusion models, providing practical strategies to improve both evaluation and unlearning performance. The ability to remove the influence of training samples from a learned model, often referred to as machine unlearning (Bourtoule et al., 2021), has become increasingly important. Regulatory frameworks such as the "right to be forgotten" in the General Data Protection Regulation (GDPR) by the European Union and growing concerns about sensitive or proprietary data have created demand for methods that allow models to forget without costly retraining from scratch. Recently, with the development of generative models such as diffusion models (Ho et al., 2020), unlearning the unsafe concept or memorization has been actively explored through training-free sampling (Kim et al., 2025), output filtering (Y oon et al., 2025), and fine-tuning (Wang et al., 2025a).

Recent work has shown that diffusion models memorize and reproduce training data examples. At the same time, large copyright lawsuits and legislation such as GDPR have highlighted the need for erasing datapoints from diffusion models. However, retraining from scratch is often too expensive. This motivates the setting of data unlearning, i.e., the study of efficient techniques for unlearning specific datapoints from the training set. Existing concept unlearning techniques require an anchor prompt/class/distribution to guide unlearning, which is not available in the data unlearning setting. General-purpose machine unlearning techniques were found to be either unstable or failed to unlearn data. We therefore propose a family of new loss functions called Subtracted Importance Sampled Scores (SISS) that utilize importance sampling and are the first method to unlearn data with theoretical guarantees. SISS is constructed as a weighted combination between simpler objectives that are responsible for preserving model quality and unlearning the targeted datapoints. When evaluated on CelebA-HQ and MNIST, SISS achieved Pareto optimality along the quality and unlearning strength dimensions. On Stable Diffusion, SISS successfully mitigated memorization on nearly 90% of the prompts we tested.

Biological neurons have adaptive nature and perform complex computations involving the filtering of redundant information. Such processing is often associated with Bayesian inference. Yet most common models of neural cells, including biologically plausible, such as Hodgkin-Huxley or Izhikevich do not possess predictive dynamics on the level of a single cell. The modern rules of synaptic plasticity or interconnections weights adaptation also do not provide grounding for the ability of neurons to adapt to the ever-changing input signal intensity. While natural neuron synaptic growth is precisely controlled and restricted by protein supply and recycling, weight correction rules such as widely used STDP are efficiently unlimited in change rate and scale. In the present article, we will introduce new mechanics of interconnection between neuron firing rate homeostasis and weight change by means of STDP growth bounded by abstract protein reserve, controlled by the intracellular optimization algorithm. We will show, how these cellular dynamics help neurons to filter out the intense signals to help neurons keep a stable firing rate. We will also examine that such filtering does not affect the ability of neurons to recognize the correlated inputs in unsupervised mode. Such an approach might be used in the machine learning domain to improve the robustness of AI systems. Modern neural networks and deep learning systems still lack the generalization and self-learning abilities of natural brains. Also, deep neural nets (DNN) need a lot of labeled data. Being tuned for one particular task and dataset DNNs may not perform so well in real practical application. These are major obstructions in the widespread implementation of deep learning systems for practical use [1]. Yet, training of SNN still needs to be improved to be widely used.