Modern datasets in neuroscience enable unprecedented inquiries into the relationship between complex behaviors and the activity of many simultaneously recorded neurons. While latent variable models can successfully extract low-dimensional embeddings from such recordings, using them to generate realistic spiking data, especially in a behavior-dependent manner, still poses a challenge. Here, we present Latent Diffusion for Neural Spiking data (LDNS), a diffusion-based generative model with a low-dimensional latent space: LDNS employs an autoencoder with structured state-space (S4) layers to project discrete high-dimensional spiking data into continuous time-aligned latents. On these inferred latents, we train expressive (conditional) diffusion models, enabling us to sample neural activity with realistic single-neuron and population spiking statistics. We validate LDNS on synthetic data, accurately recovering latent structure, firing rates, and spiking statistics. Next, we demonstrate its flexibility by generating variable-length data that mimics human cortical activity during attempted speech. We show how to equip LDNS with an expressive observation model that accounts for single-neuron dynamics not mediated by the latent state, further increasing the realism of generated samples. Finally, conditional LDNS trained on motor cortical activity during diverse reaching behaviors can generate realistic spiking data given reach direction or unseen reach trajectories. In summary, LDNS simultaneously enables inference of low-dimensional latents and realistic conditional generation of neural spiking datasets, opening up further possibilities for simulating experimentally testable hypotheses.

翻译：现代神经科学数据集为探究复杂行为与大量同步记录神经元活动之间的关系提供了前所未有的可能性。虽然隐变量模型能够成功地从这类记录中提取低维嵌入，但利用它们生成真实的脉冲数据（尤其是以行为依赖的方式）仍具挑战性。本文提出神经脉冲数据隐扩散模型（LDNS），这是一种基于扩散的生成模型，具有低维隐空间：LDNS采用带有结构化状态空间（S4）层的自编码器，将离散的高维脉冲数据投影到连续时间对齐的隐变量中。在这些推断出的隐变量上，我们训练了表达能力强的（条件）扩散模型，从而能够生成具有真实单神经元与群体脉冲统计特性的神经活动数据。我们在合成数据上验证了LDNS，准确恢复了隐结构、发放率和脉冲统计特性。接着，我们通过生成可变长度的数据来模拟人类在尝试言语期间的大脑皮层活动，展示了其灵活性。我们进一步展示了如何为LDNS配备一个表达能力强的观测模型，该模型能够解释不由隐状态介导的单神经元动态特性，从而进一步提升生成样本的真实性。最后，在不同伸手行为期间的运动皮层活动数据上训练的条件LDNS模型，能够在给定伸手方向或未见过的伸手轨迹时生成真实的脉冲数据。总之，LDNS同时实现了低维隐变量的推断和神经脉冲数据集的条件生成，为模拟可通过实验检验的假设开辟了更多可能性。