diff --git a/common/common.cpp b/common/common.cpp
index 5f10718ec..192182d05 100644
--- a/common/common.cpp
+++ b/common/common.cpp
@@ -1590,6 +1590,9 @@ static ggml_type kv_cache_type_from_str(const std::string & s) {
     if (s == "q4_1") {
         return GGML_TYPE_Q4_1;
     }
+    if (s == "iq4_nl") {
+        return GGML_TYPE_IQ4_NL;
+    }
     if (s == "q5_0") {
         return GGML_TYPE_Q5_0;
     }
diff --git a/ggml-cuda.cu b/ggml-cuda.cu
index 64ee243be..14d021ac8 100644
--- a/ggml-cuda.cu
+++ b/ggml-cuda.cu
@@ -6831,6 +6831,54 @@ static __device__ void cpy_blck_f32_q5_1(const char * cxi, char * cdsti) {
     memcpy(dsti->qh, &qh, sizeof(qh));
 }
 
+static __device__ __forceinline__ int best_index_int8(int n, const int8_t * val, float x) {
+    if (x <= val[0]) return 0;
+    if (x >= val[n-1]) return n-1;
+    int ml = 0, mu = n-1;
+    while (mu-ml > 1) {
+        int mav = (ml+mu)/2;
+        if (x < val[mav]) mu = mav; else ml = mav;
+    }
+    return x - val[mu-1] < val[mu] - x ? mu-1 : mu;
+}
+
+static __device__ void cpy_blck_f32_iq4_nl(const char * cxi, char * cdsti) {
+    const float * xi = (const float *) cxi;
+    block_iq4_nl * dsti = (block_iq4_nl *) cdsti;
+
+    float amax = 0.0f;
+    float vmax = 0.0f;
+
+    for (int j = 0; j < QK4_NL; ++j) {
+        const float v = xi[j];
+        if (amax < fabsf(v)) {
+            amax = fabsf(v);
+            vmax = v;
+        }
+    }
+
+    float d = vmax / kvalues_iq4nl[0];
+    const float id = d ? 1.0f/d : 0.0f;
+
+    float sumqx = 0, sumq2 = 0;
+    for (int j = 0; j < QK4_NL/2; ++j) {
+        const float x0 = xi[0        + j]*id;
+        const float x1 = xi[QK4_NL/2 + j]*id;
+        const uint8_t xi0 = best_index_int8(16, kvalues_iq4nl, x0);
+        const uint8_t xi1 = best_index_int8(16, kvalues_iq4nl, x1);
+        dsti->qs[j] = xi0 | (xi1 << 4);
+        const float v0 = kvalues_iq4nl[xi0];
+        const float v1 = kvalues_iq4nl[xi1];
+        const float w0 = xi[0        + j]*xi[0        + j];
+        const float w1 = xi[QK4_NL/2 + j]*xi[QK4_NL/2 + j];
+        sumqx += w0*v0*xi[j] + w1*v1*xi[QK4_NL/2 + j];
+        sumq2 += w0*v0*v0 + w1*v1*v1;
+    }
+
+    dsti->d = sumq2 > 0 ? sumqx/sumq2 : d;
+}
+
+
 template <cpy_kernel_t cpy_blck, int qk>
 static __global__ void cpy_f32_q(const char * cx, char * cdst, const int ne,
                                  const int ne00, const int ne01, const int ne02, const int nb00, const int nb01, const int nb02,
@@ -8586,6 +8634,17 @@ static void ggml_cpy_f32_q5_1_cuda(
         (cx, cdst, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13);
 }
 
+static void ggml_cpy_f32_iq4_nl_cuda(
+    const char * cx, char * cdst, const int ne,
+    const int ne00, const int ne01, const int ne02, const int nb00, const int nb01, const int nb02,
+    const int nb03, const int ne10, const int ne11, const int ne12, const int nb10, const int nb11, const int nb12, const int nb13, cudaStream_t stream) {
+
+    GGML_ASSERT(ne % QK4_NL == 0);
+    const int num_blocks = ne / QK4_NL;
+    cpy_f32_q<cpy_blck_f32_iq4_nl, QK4_NL><<<num_blocks, 1, 0, stream>>>
+        (cx, cdst, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13);
+}
+
 static void ggml_cpy_f16_f16_cuda(
     const char * cx, char * cdst, const int ne,
     const int ne00, const int ne01, const int ne02, const int nb00, const int nb01, const int nb02,
@@ -10986,6 +11045,8 @@ static void ggml_cuda_cpy(ggml_backend_cuda_context & ctx, const ggml_tensor * s
         ggml_cpy_f32_q4_1_cuda(src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
     } else if (src0->type == GGML_TYPE_F32 && src1->type == GGML_TYPE_Q5_0) {
         ggml_cpy_f32_q5_0_cuda(src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+    } else if (src0->type == GGML_TYPE_F32 && src1->type == GGML_TYPE_IQ4_NL) {
+        ggml_cpy_f32_iq4_nl_cuda(src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
     } else if (src0->type == GGML_TYPE_F32 && src1->type == GGML_TYPE_Q5_1) {
         ggml_cpy_f32_q5_1_cuda(src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
     } else if (src0->type == GGML_TYPE_F16 && src1->type == GGML_TYPE_F16) {