To address the limitations of backpropagation, which relies on global gradient synchronization, this paper presents Stochastic Layer-wise Learning (SLL), a layer-wise training algorithm that performs layer-wise coordinated updates while maintaining global representation consistency. Inspired by Evidence Lower Bound (ELBO) and based on Markov assumptions about networks, SLL allows each layer to optimize a local objective via a deterministic encoder. ELBO's intractable KL divergence is replaced by a Bhattacharyya surrogate computed from an auxiliary categorical posterior distribution derived through a random projection that maintains fixed geometry. Optional multiplicative dropout provides probabilistic regularization. SLL eliminates backpropagation between layers by optimizing locally and aligning globally. Experiments on MLPs, CNNs, and Vision Transformers, ranging from MNIST to ImageNet, show that SLL outperforms recent local methods, while its memory footprint rivals that of global BP, regardless of depth.