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Diffusion language models (dLLMs) generate text by iteratively denoising a masked response and can commit multiple output positions per model invocation. Their bidirectional attention prevents exact autoregressive-style KV caching, since committing one position shifts the KV activations of all others. Approximate caching techniques such as Fast-dLLM and dKV-Cache refresh KV activations repeatedly and reuse them across intervening decodes, inducing a repeated prefill/decode structure. This makes AR serving mechanisms relevant to dLLMs, but not directly applicable. dLLM decodes are block-sized rather than token-sized, prefills recur, and bidirectional attention precludes the chunked prefill mechanism used for stall-free colocated serving. We present Sangam, a serving system for cached dLLM inference. Sangam introduces a deficit token-budget scheduler that admits in-flight decodes first, admits whole indivisible prefills only when the accumulated token budget allows, and carries unused budget forward. This achieves amortized stall-free scheduling. Disaggregated serving avoids prefill-decode interference but suffers from prefill/decode resource partitioning problem. Sangam adopts a hybrid serving strategy, overflowing prefills onto decode workers to relieve prefill under-provisioning, and uses the same deficit-budget scheduler to protect those workers' decodes from the overflow. We show that like AR serving, dLLM serving design space is governed by prefill-decode interference and prefill/decode partitioning. Colocated serving is most effective on decode-heavy workloads, cutting mean latency by 9-20% over hybrid execution on LLaDA-8B ShareGPT; while hybrid execution is most effective on prefill-heavy workloads, cutting mean latency by 8-20% over colocated execution on Dream-7B arXiv. Sangam is available at this https URL.