COVPW-RPC: CERTIFIED RELATION-PRESERVING CORRELATION CONTROL FOR PAIRED TIME-SERIES GENERATION

Realistic individual time series can form an unrealistic pair. Correcting their comovement may also destroy a relation that the sample already captures. We propose CovPW-RPC, a post-sampling controller for paired diffusion generation. It preserves the declared relation and scales only centered common increments. An exact, monotone response maps this scale to log-return correlation. Its inverse selects the smallest feasible edit toward a target interval, subject to action and energy limits. Targets can be training-set constants or predictions from observed context; the action adapts to each generated path. No generator retraining is required. Identical-draw tests reduce rolling-correlation distribution error on all 15 financial pairs and all ten weather-station pairs. A prospective test on 12 assetdisjoint financial pairs reduces this error by 38.52%. Simple training targets retain over 98% of that gain, supporting the value of the path-dependent inverse. A retrospective fixed-scale comparison further isolates this benefit. The unchanged controller also improves a second diffusion construction. On GRU samples, the frozen policy fails, while a distribution-targeted extension improves development and retrospective temporal results. Exact relation preservation coexists with empirical variance, tail and cointegration tradeoffs. The contribution is a tractable control mechanism: specify what a generated path must retain, expose what it can change, and measure the quality of the resulting edit.