This note introduces Projected Microbatch Accumulation (PROMA), a reference-free proximal policy method that controls KL divergence by projecting away high-variance components of the policy gradient. Two variants are presented. In the accumulation-based variant, the running gradient is projected orthogonal to the sequence-wise log-probability gradients of each microbatch. In the intra-microbatch variant, a factored projection using dominant subspaces of activations and gradient outputs is applied independently within each microbatch, making it compatible with standard data-parallel training. Empirically, the accumulation variant achieves tighter per-step KL control than GRPO with PPO clipping, while the intra-microbatch variant achieves the best validation performance.