Deep Neural Network (DNN) inference is emerging as the fundamental bedrock for a multitude of utilities and services. CPUs continue to scale up their raw compute capabilities for DNN inference along with mature high performance libraries to extract optimal performance. While general purpose CPUs offer unique attractive advantages for DNN inference at both datacenter and edge, they have primarily evolved to optimize single thread performance. For highly parallel, throughput-oriented DNN inference, this results in inefficiencies in both power and performance, impacting both raw performance scaling and overall performance/watt. We present Proximu$\$$, where we systematically tackle the root inefficiencies in power and performance scaling for CPU DNN inference. Performance scales efficiently by distributing light-weight tensor compute near all caches in a multi-level cache hierarchy. This maximizes the cumulative utilization of the existing bandwidth resources in the system and minimizes movement of data. Power is drastically reduced through simple ISA extensions that encode the structured, loop-y workload behavior. This enables a bulk offload of pre-decoded work, with loop unrolling in the light-weight near-cache units, effectively bypassing the power-hungry stages of the wide Out-of-Order (OOO) CPU pipeline. Across a number of DNN models, Proximu$\$$ achieves a 2.3x increase in convolution performance/watt with a 2x to 3.94x scaling in raw performance. Similarly, Proximu$\$$ achieves a 1.8x increase in inner-product performance/watt with 2.8x scaling in performance. With no changes to the programming model, no increase in cache capacity or bandwidth and minimal additional hardware, Proximu$\$$ enables unprecedented CPU efficiency gains while achieving similar performance to state-of-the-art Domain Specific Accelerators (DSA) for DNN inference in this AI era.